I bought the pink Hello Kitty version for my then 5 year old daughter four years ago. It sounds pretty decent. I really should replace the tuners though.
Many years ago I used to play a great playing and sounding LP Custom from '77 or '78. It was very heavy however.
The jazz models like the L5, Super V and Super 400 from the Norlin era also have a somewhat lesser reputation. Like with the LP's, this doesn't mean that they didn't make good...
Have you thought about a Tom Anderson Classic (or a Suhr) with the right specs? Great examples do pop up in the emporium. I bought a great Anderson Classic with a 1-11/16" chunky neck in olympic white used for less than a Custom Shop Fender.