I was thinking that maybe the best potential for a spinoff movie is a new crew in the current Abramsverse, at the same time frame as nuKirk etc. On a different ship perhaps? It would allow the possibility for a crossover between the two and both of them borrowing cast members from each other in future movies.
This is instead of jumping ahead 80 years and losing the ability to crossover.
The other option is to simply put all the TNG era characters and ships into the TOS era, this would not be explained away by a simple timeline divergence and would cement the nuVerse as a true reboot that gives all the characters from every era the chance to interact.