I keep checking every day, and the same thing is still going on. The slave zones seem to be getting updated when I change the serial number on the masters, but I keep getting "dumping master file: tmp-eoC1UgYwOE: open: permission denied" like errors on all of them.
The only thing I haven't tried for a while is the suggestion to move all the slave zone files to a different directory. I tried it once before, but it didn't work at all. No updates were getting through anytime. I might have had the file permissions wrong at the time though. I still would rather not do that if possible because I like the setup as it is now.
This really is frustrating, especially since nothing seems to be wrong.