I doubt the dial is aftermarket. Just a cursory Google Image search for 5626-7111 will reveal a couple of examples with -7110T dials, as well as examples with -7110R dials. Perhaps the -7110T dials were Seiko service dials? Because the -7110T dials appear only on -7110/7111/7113 models, and AFAIK the -7110T dial doesn't come from any other 56KS model.
It started off with the 5626-7110 with the monocoque case, which evolved to the 5626-7111 with the KS-signed screw-on caseback, which then evolved to the 5626-7113 with the plain screw-on caseback. I can't verify your claim about the -7111 and -7113 crowns, but it's not something that would surprise me, it sounds decently plausible.
350 USD doesn't sound terrible. The watch appears to be in decent condition. Does the watch look like its been rebuffed/repolished (since some of the lines don't as sharp) or is that just the pictures being blurry? It certainly looks better than many other examples on the market.