Electric suggestions between US$750 and US$1500ish

I'm currently considering upgrading from my current electric guitar, a dirt cheap beginner's Epiphone Les Paul (it's the next model up from the Model 100).

I've set a budget of about $1500, just to keep myself from going hog wild. I have very large hands, play a fair number of dad rock covers mostly, and occasionally derp around with a few other musicians in the neighborhood.

I've played around with and liked both the standard Mexican Stratocaster, and found the PRS Custom 24 to be an enjoyable guitar to play. I'm wondering if there's another model I need to consider, as I'm planning this as a Christmas present to myself.