As far as subtle changes in the Enterprise's looks affecting the average movie goer goes, I wonder how many of them who saw ST09 and STID even really took notice of the new uniforms in STB.
The idea of any in-universe answer to it does tend to contradict the idea of the lonely five-year mission into deep space. Then again, they were mostly around colonies and star bases in familiar space in TOS, too. So maybe they weren't "out there" exploring quite as much as we'd think. I'd say the ship was modified at a star base around the same time they put in for an extended leave and that's when they also got the new uniforms. Works for me. Starfleet's version of FedEx delivered the things there from a ship yard, and the updates/modifications were made.
Since the Enterprise never really had a shakedown cruise in ST09, being immediately called into service, it's also likely so many modifications happened over such a short time because bugs were found as the ship was being used in service and modifications had to be done on the fly. No doubt Scotty proposed some changes, too. Also, technology seems to have advanced quicker in the new timeline, so technological changes would come about quicker, too. If the Enterprise is the flagship of Starfleet in this universe, then it stands to reason it would have the most updated equipment installed as soon as it was possible to install it.