So I was just in the shower thinking (as you do) and what if Picard, Sisko etc weren't 100 years in the future. What if they were in the same Century?
Say you did a TOS (or all Trek, with Enterprise still as the prequel) reboot, then obviously things would be different. Over seven seasons, relations with the Klingons would nearly lead to war then potentially improve and maybe the Khitomer Accords would be signed in the show's finale - rather than rush rush rush to sync with what we learnt in TNG. The Romulans are slightly easier - ever since the Romulan Wars they've been a bit recluse behind the Nuteral Zone.
So Picard, half way through the 5 Year Mission becomes Captain of the Excelsior, then somewhere down the line maybe an Enterprise as Sulu takes his ship. Worf would possibly be a renegade Klingon who convinces Starfleet to take him on, or he can be a version of General Worf from TUC.
Races such as the Ferengi, Cardassians, Bajorans, Betazed etc would be made First Contact with, and the Federation set up an outpost on an abandoned Cardassian space station calling it Deep Space Nine. A starship called Voyager is lost in the Badlands during it's maiden voyage.
Yuo get my drift. You start with a TOS reboot then in Year 3 start Excelsior. It's all about the CHARACTERS of Star Trek.
All in a period where Kirk and possibly Pike are Captain of the Enterprise on the first two missions or so, the other popular characters also exist. No More TOS vs TNG - TOS has got the focus ever since I say the New Voyages fan film got popularm but TNG still has a huge fanbase. A bit like the Marvel/DC Universes. So, they can all be involved in shared story arcs like how the books do Destiny/Typhon Pact.
I've seen reboot ideas where Saavik, Demora Sulu and even Admiral Jellico are there at the beginning of the 5 Year Misson, so this would be similar in moving timelines round - like the DC Universe (remember there was no shared universe at the start) but you would have to make sure there is an interesting backstory/history.