All I needed was a mention of RAM. That led me to read up on the PROGMEM, so I stored a bunch of arrays there.
Then, I got curious and wanted to know how much RAM I was using/had left. I found this bit of code (can't find original source)
int freeRam ()
extern int __heap_start, *__brkval;
return (int) &v - (__brkval == 0 ? (int) &__heap_start : (int) __brkval);
I have no idea how it works, but by printing to the serial monitor I could see how much RAM I had left...pretty cool!
Overall, was able to save more than 260 bytes by moving stuff to PROGMEM. Regardless, the ATtiny44 is not going to be a good choice, but the 84 works great.