Well, I'm not out of the woods yet. It looks like I haven't been able to change the clock frequency or something. Instead of running at 8MHz, it seems to be running at 1MHz, but still running the program as if it was running at 8MHz. For example, delay(1000) takes 8 seconds, instead of 1.
Like I said, there is an error when I try to Burn the Bootloader in Arduino-0022. Here's the verbose output of that error: http://pastebin.com/7D9GYimW
Incidentally, if I select "ATtiny85 at 1MHz (internal oscillator; BOD disabled)", then delay(1000) takes 1 second, as it should. I would try burning the 16MHz bootloader with an external oscillator, but I'm not sure how to connect the oscillator to the ATtiny.
Programming ATtiny's at 1MHz is cool, but it would be nice to have a faster clock for serial support, etc. If I can just get that clock frequency changed, I'm good to go.