I don't know if this helps at all, but i also use my thumb to mute the lower strings. It just seems the easiest way to do it. Also, Tom Hess does it this way and he sounds just as clean as anyone when he plays fast.

As for muting the higher strings, I don't really deliberately try to do so, as I've never had too much of a problem with them ringing out. But then I noticed that I'm usually fretting on the lower strings, and as I do so, the middle of my fingers kind of rest on the higher strings which mutes them. For a while I didn't even realize I was doing it! Talk about lucky.

Now sweep picking, I'll actually take any advice I can on the matter, but recently I've had a major breakthrough in muting the lower strings while ascending when sweep picking. I basically hold my hand in a very particular angle (it took a lot of trial and error to figure it out) so that as I go to sweep pick across the next string, the part of my palm next the my thumb mutes the string I just played. As long as I keep my hand in this angle, it mutes each string right as I'm ready to play the next one. I hope that makes sense! Does anyone else do something similar?

~Rusty