First, have you seen a pinout for this part? I'm guessing it is the same as every other TO-220 package, but I'd rather not guess. Anyway, the gate charge is 27nC. I'm just going to guess that the time interval is in the same unit scale (nano) as Coulombs is. That really doesn't make sense, but up to 270us is acceptable because I can easily compensate for that. More than a us and I might start to wonder if higher current wouldn't be a bad idea. The gate only needs an peak 10mA of current, with a hold of 1mA. I think I'll use some diodes to drop the current to 7V. Two or three should be fine for that, right? Also, shouldn't I^2 be somewhere in power dissipation? I know it was for MOSFETS.
So do you mean caps on the high voltage side or the low voltage side or both? Could I use many nanofarad caps because (AFAIK) lower capacity has a lower time constant? Say, 5-10 100nF caps? Of course, now that I re-read your post, I see that you said I should use 100nF caps. Wouldn't that keep the gate on longer than without caps? Also, I am still using the IGBT with a gate driver, so it has 1.5A (1A because of the regulator) available.
Random tangent, but why do inductors try to maintain current flow? Thinking about Ohm's Law, it makes sense that there is a voltage rise, but why does it try to maintain current levels?