I tend to go with Timo
on this one: The 1701-A wasn't a new build, just an older ship renamed.
By the time of STII the Enterprise was busted down to a training ship. It's possible that the 1701-A was another ship used for training or heading to the breakers.
I've always thought that the 1701-A was a PR move on the part of Starfleet: a nice quiet, safe command, on a "historic" ship, that he could ride into retirement with--the sooner the better.