using a compressor to make your single coil tones have a similar volume to your humbucking tones will mean you lose a lot of the dynamics that make ss tones really good (that is unless you are going for a nashville country sound - and im guessing not).
I tend to agree with an earlier post that having a few sounds that are less powerful is a good option in a live setting, but i can understand where you are coming from tho.
The posts about using compressors in the studio to match volumes is not strictly speaking true either...the compressors are usually used to smooth of excessive dynamic leaps. The art of mixing is the recording engineers way of making things level (especially in this modern age of automation) via the use of the faders.
Okay so how do we give you everything you are after in a live setting without installing higher outpout ss pickups in your guitar? The first answer lies in your pedal board. With a regular analog pedal style rig then you may need to have a booster dedicated to just doing exactly what you are after. The MI audio boost and buff is a good unit and its inbuilt buffer goes a long way to recovering your signal loss from using a bunch of pedals. At its higher levels it turns more into a treble boost like circuit, but i think you are onky after a mild level increase without losing your ss character right? Other units like the mxr micro amp or the EH lpb will work well also. Of course there is the sd pickup booster too which is really good.
Or go with a totally different approach....and this may suit you cos it seems you are the kind of player who wants a lot of sounds all set up and ready with the flick of a switch....get hold of something like a TC nova system and have all your tones and levels pre programmed. One smallish box with all the sounds most ppl need and very few cables. Analog drive sounds. Beautiful reverbs etc and no crappy modelling emulations mean you can make the most of your nice axe and amp tones. Also if you are still hell bent on using a compressor the option is there, but you are not limited to squashing up your entire sound juts for the sake of keeping levels matched..you can use it as a tewtural effect or a bit of seasoning which is what compressors do best anyway. Definitely check one out.