Free strokes is primarily how people do it- I've attempted playing it with all rest strokes, and it was neither easy, fluid, or fun. I do rest my thumb on the next string quite often after plucking with it, similar to using a floating thumb technique to help mute the lower string, but performing rest strokes with the other fingers was always counterproductive. When I want a really thick sound, I often do rest strokes using just my ring finger. For the most part though, my free strokes don't sound much different at all compared to my rest strokes- that may be a combination of the fact that I've practiced it a lot and because my rest stroke playing was never that thick/thumpy to begin with. You'll find that your hand placement and the attack you use/setup you have will alter the sound quite a bit when using free strokes, so may have to work on finding a setup/attack that gives your free strokes a similar tone to your rest strokes.
I cover several ways of muting when using this technique in a couple of videos- here are the links if you haven't seen them yet: