I'm all for modifications too, i love how Jags look but hate how they can be restricting in stock form.
Depends what sort of 'fat' sound you want, you can achieve so much. People like J Mascis and Billy Corgan achieved heavy thick sounds with single coils by using fuzz pedals.
Fuzz is more single coil friendly than distortion.
But if you're looking for a more compressed heavy metal sound you'll have to go with something like a JB Jr or even try a multi effects that should give you the option of a noise gate to help prevent microphonic feedback and tonally shape the low end frequencies. I think the guy in NIN uses multi effects with his Jazzmasters and Cyclone II.
There are other things to consider here though like the construction and timber used. You just aint gonna get the sound of a Les Paul with a Mustang.