That's just way too complicated in my opinion. I'm still partial to my idea that only Cage looked like SNW aesthetics (due to the crews' minds being messed with from Rigel VII, we're seeing the action from their perspective where it's not entirely accurate), and there just was a refit of the Enterprise (and maybe other Constitution class ships) between SNW and TOS. Probably for the galactic barrier mission; as I mentioned before maybe all that fancy tech on the SNW Enterprise would've blown up outright and "retro" tech had to be installed and they just left it that way after WNMHGB.