Frankly, I'd recommend you upgrade your Squier to a Fender HSS instead of swtching to a HH guitar.
I modified my squier, and Im so happy with it I dont think I need a fender, I switched the pickups for a wilkinson HSS kit, got grover heads, some Graph Tech saddles and gave it a vitage look to the body and hardware, plus I took one of the tones off and installed individual volumes to the single coils and the hum... this way each one has the pots they deserve... I mean a 500k for the hum and a 250k for the sc... only the humbucker has tone control... its pretty special...
Im just looking for a second guitar and I like the LP look...
Thanks for the recomendation anyway...