I would do a reboot.
I would also eliminate the maquis premise, and just make Voyager a purely federation ship and crew. I would also eliminate the Caretaker angle that brought Voyager to the Delta Quadrant. The way Voyager was stranded in the DQ is actually because the federation discovered a new transwarp conduit network, much like as seen in End Game. Facing a pending Borg invasion force, rather than wait for other Federation ships to arrive and assist Voyager, Janeway commands her crew to to close the conduit by collapsing it within by taking voyager into the transwarp conduit, and firing photon torpedoes to collapse it. The plan worked and destroyed the transwarp network, but at a cost: the Voyager was sucked into the transwarp conduit, and ended up in the DQ (basically, the reverse of how Voyager got home in Endgame).
USS Voyager
Still an Intrepid Class ship, it would be largely unchanged. However, during the course of the series, I would like to see the ship deteriorate. It would start out shiny, new, and state of the art, but as time went on, battle damage and wear and tear would gradually accumulate, and the physical appearance of the ship would reflect that. Also, energy would be rationed, so luxuries like holodecks and replicated items would be severely rationed.
Captain Katherine Janeway
Newly promoted to captain. Young, inexperienced, and arrogant, having made captain at age 34. She is an engineering and tactical genius, but is a bit of a hot head, and can be brash. Externally, she exudes confidence, but internally, she's very unsure of herself and her decisions. She is more directly at fault for stranding Voyager, due to a brash and arrogant decision than the original series. This decision causes much friction on her ship, and many people don't respect her at first, including Chakotay. Through the course of the show, she is humbled, and learns to become a true and respected leader.
Cmdr Tuvok, First Officer and Science officer background
As with the series, he is a Janeway's mentor and former instructor from Starfleet academy. Rather than security, I would change Tuvok's occupation to science officer, as a Vulcan should be. I would age Tuvok further, making him around 165, having served aboard the Excelsior under Captain Sulu . Rather than have him take a break from Starfleet, he is credited as one of the longest serving officers in Starfleet history. Though a capable leader, and he acts as a father figure to the crew, he has turned down captaincies of his own, by personal choice, and prefers not to be in the forefront. He is much happier as second in command. Tuvok's personality would largely be the same, but more patient, and very wise.
LT Cmdr Tarak Ka-e-te-nay, AKA "Chakotay" Second officer and Tactical background
"Chakotay," an Apache, is a battle-hardened starfleet veteran of the Cardassian Border Wars, and is older at 57 years old. He is much respected for his tactical and strategic expertise, and his bravery in battle. His name literally means Warrior in Apache (it really does, actually). He goes by "Chakotay," to honor his best friend, an Andorian starfleet officer who died saving his life, during the Cardassian Border wars. Chakotay was a corruption/mispronunciation of Tarak Ka-e-te-nay's first and last name by the Andorian star fleet officer he served with.
Chakotay was formerly a distinguished Captain, who sympathized with the Maquis, during the Maquis rebellion, after uncovering the atrocities committed by Cardassians on federation settlers in the DMZ. During one incident, he intervened by entering the DMZ against orders. In this incident, the Cardassians were about to wipe out a federation colony that refused to leave after the treaty was signed, until Chakotay intervened by putting his ship between the planet and the Cardassians. While war was averted through diplomacy and negotiations, and there was no loss of life, because he violated Admiral Necheyev's orders, she made him a scape goat. He was stripped of command and reduced to LT Cmdr. Chakotay's service record prior to this event was exemplary, which is why he was only relieved of command and demoted, and not releived of duty, permanently. Chakotay was a last minute addition to the Voyager crew, and really didn't want the assignment, and was even considering retiring from Starfleet at the time Voyager was stranded.
Janeway respects Chakotay's council on tactical matters. Unfortunately, Chakotay does not have much respect for Janeway, as he finds her inexperienced, overconfident, and reckless, which is ironic since Chakotay had a reputation for being a reckless himself, when he was her age. Tuvok often has to reign Chakotay in, when he clashes with him, or Janeway. Chakotay's much more hawkish and warlike, and his one flaw is that he has a prejudice against Cardassians, based on what he has seen in war. The irony is he is madly in love with Seska, who is secretly a Cardassian spy.
LT Cmdr Seska, communications officer (and spy for the Cardassian Union)
Seska is a Cardassian spy, surgically altered at the genetic level (gene re-sequencing) to appear human. As a consequence, of this procedure, Seska finds that her DNA is actually BECOMING human, and she is having to deal with human emotions,and is losing touch with her Cardassian self. THis is actually slowly driving her insane, over the course of the show.
Her mission was to gather intel on the newly-launched USS Voyager, and steal some of its technology. However, this mission was put on hold when Voyager ended up in the delta quadrant. Seska is the lover of Chakotay, though he is unaware of her true heritage. Seska often eggs Chakotay on, giving him ideas that he ought to lead a mutiny, and replace Janeway as captain. Her true motive is that if Chakotay is captain, she can control Chakotay, and possibly bring the Cardassians the USS Voyager, should they ever make it back to the Alpha quadrant. Chakotay is by the book, but since he has nearly 15 years as a starfleet captain, he thinks Seska may have a point, and is starting to consider a mutiny.
The Doctor:
I still like the idea of the doctor being an EMH on extended duty. I wouldn't do much to change his personality and depiction, at all. However, since he is a hologram, he could change his appearance. I like the idea of if he were to use a treatment pioneered by McCoy, he could appear as McCoy to deliver said treatment.
LT Cmdr B'elanna Torres, Chief Engineer
B'elanna would largely remain unchanged, however, I think I would change her background. Rather than being from a broken home where her dad ran away, instead, her father was killed by a her Klingon uncle as an "honor killing," because he married B'elanna's mother without his approval. Her mom was a Klingon outcast because she married a human AND she followed an engineering path, instead of a warrior career track. Both her parents were engineers, and as a result, B'elanna became an even more brilliant engineer. B'elanna's mother raised her alone and she would have been much like Keh'leyr in personality. It was the murder of B'elanna's father, and witnessing how other Klingons treated her and her mother over the years, that caused B'eLanna to reject Klingon society. B'elanna would gradually accept her Klingon heritage, as the series progressed.
Replace LT Tom Paris with Chief Helmsman Nick Locarno
Rather than a convict, I would replace Paris with Locarno. Personality wise, it would be about the same. But with a different backstory for the character. It would be revealed that Locarno was drummed out of starfleet officer school. However, with a word from an old friend of his father, Admiral Paris, Nick Locarno was able to enlist in starfleet, and worked his way up as an enlisted chief helmsman, in large part due to his piloting skill.
Kes and Neelix
I would omit Kes' 5 year lifespan right off the bat, as it is too restrictive, and Kes and Neelix would not be a couple. Kes and Neelix would be a civilian members of the crew, picked up in the DQ, and were rescued prior to Neelix's ship blowing up . Kes' people would be unknown to her, as she was separated from them when she was a baby for unknown reasons, and raised by Neelix. She would slowly learn of her powers, which eventually would grow to the point where she ascends to a higher plane of existence. Kes would be an unofficial ships councilor, and would act as a nurse in times of need. Much like her personality in the show, she is kind-hearted almost to a fault, and balances out Neelix's swindler tendencies with her honesty, even scolding him at times.
Neelix would be sort of like he was originally depicted. Neelix is more of a trader, scoundrel and swindler in this series, more like a Lando Calrissian, and less like a buffoon. Neelix became Kes' foster father. Though she was raised by Neelix, the roles of the two have almost reverse, and by the time of Voyager, she acts as the mature one of the two. Neelix would be important to the crew as his negotiating skills with DQ civilizations, and ability to trade.
Seven of Nine, Civilian Science officer
Seven was actually the leader of a Borg raiding party on Voyager, just prior to Voyager collapsing the transwarp conduit, and the only one to survive the Voyager crew's counter offensive. When it was discovered she was human, the command staff was split on what to do with her, much like Hugh in TNG. However, Kes advocated that they attempt to de-assimilate Seven. Seven would stay very borg looking in the beginning. There would be no cat suits, and she would actually look like an ugly cyborg through the first couple seasons, with her appearance gradually becoming human. Like the show, Seven would eventually become Voyager's science officer.
No Harry Kim.