My Special Edition DVD has a commentary from Meyer in which he states he did indeed plan to have Kirk "had over the keys" (the phrase he used) to the new crew from TNG, until he was told that 80 years separated them.
I like going by the idea that the first two digits of the stardate indicate the year for the movies, putting Star Trek 5 at 2284, and Star Trek 6 and 2295. 11 years in service helps make the ship not seem quite so new when it is replaced...but what I really would prefer is to suggest that the Enterprise-B sequence is set a lot later that 78 years before the Enterprise-D segment of Generations. If it was say, 30 years after Star Trek 6, and 48 years before the later part of the movie, or any mount of time that makes sense to a viewer, we would have all that time for the Enterprise-A to be in service.
Games like Star Trek: Legacy show older ships as medical ships, and the Miranda class is shown as a cargo ship when it is older. There is a model shown onscreen in TNG of a Constitution class ship that has sideways nacelles and has what appear to be cargo doors where the large windows should be. The Wambundu class, like the Drake from TNG, are called light cruisers and medical transports. My theory is that this class could be the name given to Constitution class ships that were made this way or converted to this appearnace. That could give the Enterprise-A even longer to serve, under a different name and in a different role, or it could explain how the name is transfrerred to the Enterprise-B in a short time. I don't consider the Star Trek made since 2009 to be cannon, but the Entperprise-A being in the fleet museum onscreen does not mean it was never used this way, it could be that it was "restored" to its appearance under Kirk's control for museum display.
Additonally, the Shatner novels invlove the suddent planning change from an Enterprise-A that will go on to get a new crew, to an Enterprise-B that is Excelsior class, as a plot point, although mugh dicussed here does not fit into the plot line of the novels.