Go with B&B's original idea and make at least part of the early first season about Enterprise's final stages of construction and Captain Archer assembling his command crew, while laying some of the foundations with the Vulcans, Andorians, and Tellarites, as well as Terra Prime. Turn some of the focus away from the TOS-style Big Three and make the show more of an ensemble like TNG, VOY, and DS9.
Archer should have a real reason to hate the Vulcans. Make Henry Archer a civilian scientist who was testing a prototype warp engine, which went horribly wrong. The small science vessel he was on was destroyed. A nearby Vulcan ship might have been able to save the crew, but they decided not to do it because the ruptured warp core's explosion would have destroyed both ships. Risking hundreds of lives for less than a dozen would not have been logical.
Trip is a native of Mobile, Alabama, who decided to become an engineer when he was a kid, after fixing a busted engine on his father's boat during a fishing trip in the Gulf of Mexico. He should also be a little bit older than he was in the show, closer in age to Archer, with whom he became best friends after they met while working on the Warp Five project.
T'Pol was one of the first Vulcans to be born on Earth, and spent much of her youth in the Vulcan compound in Sausalito, California. This has given her a better understanding of human society, and is a major reason for her being assigned to Enterprise as an observer while the ship is returning Klaang to Qo'noS (which is about a month away, not two days). During an attack by the Orion Syndicate (working as agents of the Romulans to destabilize local space), the Enterprise's science officer is killed, and T'Pol is forced to take over. After the mission, Starfleet is pressured by the Vulcan High Command into keeping T'Pol in that position. Though her growing up on Earth has made her somewhat familiar with humanity, it has made her more ignorant of her own Vulcan heritage, which would be explored and developed over the course of the show.
Make Malcolm Reed an undercover Section 31 operative, assigned by the Section to spy on Enterprise's mission, along with whatever alien races (and technology) it might come into contact with, and prevent Enterprise from retaining any alien technology that could potentially harm humanity and Earth. He would also be a Major in the United Earth Marines (descended primarily from the Royal Marines and U.S. Marine Corps), and chief of Enterprise's security department, which is a Marine detachment.
Make Phlox a human, Doctor Philip Knox, a retired Starfleet corpsman (and veteran of the Kzinti Wars) who became a doctor and gained invaluable knowledge of alien medicine and physiology (as well as several eccentricities) during his years with the Interspecies Medical Exchange.
Revert Ensign Travis Mayweather to Lieutenant Joseph Mayweather, a lifelong Boomer who's seen more alien worlds than the rest of Enterprise's human crew combined (with the exception of the well-traveled Doctor Knox). Make him a man jaded toward space travel and meeting new aliens, who loves playing pranks on his less experienced crewmates, and seems to know many "interstellar shortcuts" that get Enterprise to her destinations faster than some of the routes on Earth and Vulcan's star charts.
Make Hoshi Sato the descendant of one of the Augment warlords who threatened the world during the Eugenics Wars. Her physical and mental abilities are not as superhuman as a full-blooded Augment's, but they're still well above the human norm, especially her mental capacity and linguistics skills. As the Enterprise's communications officer, she is also excellent with mathematics and computer programming, and almost got busted out of Starfleet for hacking a major Tellarite security mainframe (on a dare).
No Temporal Cold War. Replace the Suliban with the Orions. Turn the Xindi into the Kzinti, who were defeated and disarmed by humans during a series of wars in the 2110s and 2120s (basically the Carthage to Earth's Rome in an interstellar version of the Punic Wars). Have the perpetrators be a terrorist splinter group who seek to redeem the Kzinti people and avenge their humiliation at the hands of humanity. Make them pawns of the Romulans, who promise to help the Kzinti regain their status as a major power if the rogues help them. The first Kzinti weapon was a prototype that malfunctioned after only eight seconds of operation, destroying only a strip of land from Mississippi to Colombia, instead of much of the planet. Starfleet retrieves data from the wreckage leading to the Delphic Expanse, a lawless and largely unexplored region of space (no weird anomalies, since there are no Sphere Builders). The Enterprise heads off to track down the rogue Kzinti before they can build a new weapon.
Terra Prime would be introduced early on, though like in ENT they wouldn't reach prominence until the aftermath of the Kzinti attack. Have there be some sort of secessionist movement spreading through various human colonies, such as Mars and Alpha Centauri, headed by Terra Prime, who claim that Earth can barely defend itself, and would betray the colonies--human colonies--to aliens in exchange for its own safety.
There should be less of a focus on meeting new races and more of a focus on developing established, but little-known species like the Andorians and Tellarites (partially done in ENT, but not enough, especially the Tellarites).
