If it were me, I'd be using an angle grinder with an ultra-thin cutoff disc. You can make very nice clean and straight cuts that way and because you can make cuts fairly quickly, there isn't a whole lot of heat generated. If you had a big enough compressor (5HP, 60 gal.) a pneumatic die grinder with a thin cutoff blade is great on sheet metal, especially for smaller cuts since the blade is quite small in dia. A pneumatic shear, cutoff tool or nibbler are other options, but again, you'd need a big enough compressor.
If using a cutoff wheel, you'll be left with burrs along the cuts that can easily and quickly be cleaned up with a file. Cutting through two adjacent but separated layers of the sheet metal at the same time may or may not be difficult and the cutoff disc could potentially get away on you. Without seeing it in person, I think cutting each layer separately would be better.
I've used a sawzall on car bodies before but only for carving a shell into pieces or salvaging large sections. They're not really suitable for cutting neat holes and openings. I jigsaw can work with a metal cutting blade. Both a sawzall and jigsaw can vibrate and jump around a lot and be hard to control A plasma cutter will work but would be way too expensive for just a few cuts, but they sure are fun to use. An ultra-thin cutoff wheel really is the way to go.
If heat is causing problems, you could try some thermal paste that is used when welding thin sheet metal to prevent warpage. Goes by a variety of names and Eastwood has
Cold Shield.
Drilling holes will work but man, that's gotta be so slow and painful... :( Then you still need to cut the metal between the holes and you're left with really jagged edges that need to be cleaned up somehow.
