You want all of that versatility out of a single bridge pup and vol with no tone control or split/parallel? Let's face it, as Jeremy said, you're asking a lot from that setup...so much so that I would be willing to say IT'S NOT GONNA HAPPEN!!!
To get that kinda versatility you'd need at least a tone control and probably a split and/or parallel option. Maybe even a phase option.
But, to answer your question (as if it were legit) I'd recommend either a C5 or the C/59 hybrid.
I've heard of the C5 described as almost like a higher output 59 with less treble and more bass? The C/59 might be well on my radar then too.
As far as versatility, I'm not looking for a versatile guitar in the sense that I'll be able to go from Steve Miller to Steve Morse using nothing more than onboard controls. I'm looking for versatile in that the guitar will be a tool with just enough flexibility that I'll be able to teach myself to make my playing fit into any context.