Not sure about your last point, but I understand how you feel otherwise.I am weird, my favorite instruments were always stock and i did not really need to modify them. Maybe it is snobbism but i feel like i need to modify my P5 to get what i want out of it.
...Regarding EQ, I think it is hard to add something that is not already there.
Not everyone likes modding stuff, and there's a definite extra appeal to playing gear that's perfect right out of the box. That's why I own a Dingwall.
If everybody was satisfied with buying a Squier and having at it with a file and a soldering iron, there'd be no Foderas, no Ken Smiths, etc.
Still, the Fender Am Std isn't going to hit the spot, as it would have to be routed to take the Aguilar pickup, just like your Squier. Sounds like you need to move your sights way upward: Mike Lull, Sadowsky, Aleva Coppolo, Dingwall. I believe that these are all in the area of $3 grand to start...