I could see the refit being the TOS Enterprise because of one simple historical fact; have you ever seen the refit battleships that survived the Pearl Harbor attack? The Maryland, Tennessee, West Virginia, et.al. finished the war with a completely different appearance than original constructed. In fact the only thing that looked externally the same was the hull, just as in the case of the refit Enterprise and the TOS Enterprise.
I haven't seen the battleship refits you mention, but I'd certainly be interested in any before/after pictures that may be out there. You make a good point though.
But, even the hull of the refit Enterprise looks totally different from the TOS ship. The only similarity between the two starships is the basic shape, and even that isn't the same. I'm no expert in this stuff, but it seems that the TOS primary hull is much smaller than the refit, for example.