I've heard of Tamiya acrylics being thinned with Lacquer thinner but I have no idea how it would affect MM. Take a little in a bottle top or something and add a few drops of lacquer thinner and mix. See what happens. If it works ok, dip a brush into it and see how it spreads and dries. I'd hate to get that in my airbrush and have to clean up the mess afterwards if it didn't work.
It sounds like you might need to soak your head and spray tip in lacquer thinner to make sure there is no acylic dried in there. Also you might try thinning your acrylics a little more and see if that helps the clogging. The air coming back up into the paint cup is because it is taking the path of least resistance. It can't get out the tip so it has to go the other way.
I use acrylics almost exclusively and I push down on the trigger then pull quite a ways back every once in awhile and spray into a paper towel to keep the tip free of buildup and keep it from blobbing out on my model.