Well, I've tried some things, and I think I'm having success. I did get some agitators (Army Painter's stainless steel mixing balls) which drop right into the bottles as easily as was promised. I don't know if they're helping, but they sure don't hurt. I also got myself some non-Battletech miniatures, so I could practice on something I don't particularly care about. I threw a base coat onto a few of them today, in three different colors.
The blue thinned down beautifully, and after the first coat, I could probably have gotten away without a second. I tried a tan/sand which was also super-easy to work with. And then I went back to the red I had been working with ... just like before, I could not get it to a decent consistency. Right out of the bottle, it wouldn't flow, and also wouldn't cover. Thinning it down a little -- with water, Golden medium, or Vallejo airbrush thinner -- got it flowing a little better, but it still didn't seem to cover well. However, after a second coat, the result wasn't bad. It was really hard to work with, but the results were OK.
So, I think I'm going to try another brand of red. And, now that I'm starting to maybe get the hang of the paint consistency, I get the whole "work fast, 'cause your paint's gonna dry out, real quick" thing. When I'm trying other paints, I'm probably going to get myself a wet palette, too.