The board is wired exactly as shown here.
I think the duemilanove was holding pin 0 to LOW after programming was complete.
I switched to using "Blink" on pin 3 which is unused for programming. It seemed like the frying issue was solved, but the output was still jittering and dropping out randomly. Then I put a 10k resistor between Vcc and RESET as suggested, and the jittering was reduced, but not eliminated.
Now my question is this...Is it possible to program pins 0 and 1 as outputs without ruining the chip before the programmer is disconnected?
Can the Arduino ISP program be easily changed to hold RESET to ground after programming ends?
Would this keep the attiny from booting up and potentially solve this problem?
I'm definitely open to using another type of programmer, if that would get around this issue.