Well, I stayed up way too late working on this, but I've mostly finished soldering! I also learned a few things about skillet temperature, mainly, that it is possible for it to be too hot! Hahaha. I burned the PCB pretty badly but INCREDIBLY, so far everything is still working!
I put solder paste on half of the board, then got scared of accidentally nudging an IC out of position and decided to solder the ICs on first before continuing with the rest of the easier parts.
The IC soldering went incredibly well. I only had about 3 solder bridges. The middle of the board has started to turn brown at this point but I wasn't worried. I knew I just had to use less heat on the hot plate the second go around.
The second go around using the hot plate was pretty scary as the board started sizzling, smoking, and turning very dark brown (as you can see). I thought "OH NO, I've ruined the board and all my work is for naught!!" But I decided to solder on a few components to see how bad the damage was and WOW, everything is working so far. Both microcontrollers (AVR 644p and 328p) work, crystals work, and the LEDs (which look horrible after the burn) work too. I don't want to get overoptimistic here, but I think this board might be saved! And don't worry, I will be keeping this one for myself so no one has to worry about getting a burnt prototype board :)