If we are to take ST:Axanar as being "pan-canonical", taking in influences from all sorts of noncanon sources (after all, the very concept of the 4YW is from FASA), we may just as well include the backstory of the Constitutions, and the Enterprise specifically, as laid out in various novels and comics.
Obviously, every Trek writer has wanted to dip his or her pen in this particular inkwell, and many have managed to get published. A common theme is that the Constitutions are such important vessels that many have been sent on crucial missions even before being actually launched, and have engaged in adventures that have resulted in heavy damage. So a Constitution often needs to be launched twice, thrice or even four times!
The Enterprise is credited with three or four "false" launches in various novels and comics; the Constitution herself is said to have fought Klingons at Donatu, Axanar and whatnot basically "fresh out of the launch ramp" and was probably thrashed in each engagement thoroughly enough to require rebuilding and relaunching. And if Garth of Izar sees it fit to assign Axanar as the site of the latest repairs in order to entrap the Klingons, he can at least rest assured that the actual repairs will proceed as planned, what with Starfleet having lots of experience with such things!
As for the San Francisco thing, is that the site of construction, the name of the dockyards, or merely the homeport of the vessel? The first option is never quite confirmed; the second one need not mean that the yards would be anywhere near San Francisco; and the third would disassociate the construction with San Francisco altogether.
We do know that Constitutions are quite at home within atmospheres, and certainly have enough engine power to take off from Class M planets (heck, the Enterprise once basically takes off from a black hole!), so that doesn't exclude any options...
Timo Saloniemi