Nick,
There's actually another identical set of arrays (same structure, different data) and then a much bigger 3D array as well. This probably could all go in SRAM, but there's thought that this project could grow, and I'm trying to future proof it by just dumping all of the arrays into PROGMEM. I copied this setup from the Arduino PROGMEM example, here: PROGMEM - Arduino Reference.
One thought, would it work to have the Array of Arrays (aka, array of pointers) as a regular variable, but leave the longer Arrays in PROGMEM? Like I said, I was just following the example as best I could so I assumed it was easier for everything to be PROGMEM, but now I'm not sure.