OK, I just updated Kontakt (and MPT!) and now Kontakt is telling me that it doesn't have "Memory locking", and wants admin privileges... I do have admin privileges, needless to say. This is when I try to run it straight from MPT (which still just freezes it), and when I run it from within Chainer.
The dropped notes are the worst the first time I load and play through the module: after that, it seems to get a bit better. I'm assuming that this is because Kontakt's had a chance to load up all the buffered stuff and grab it somehow, but the first play through still has lots of dropped notes, even when I tell it to preload 320KB of prebuffer and use as much RAM as it wants...
Edit: I managed to alleviate the problem somewhat by forcing Kontakt to never kill voices. However, I'm still using an old version of mpt: I can't use the newest one without all sorts of dropouts.