Okay, here's an update and my advice to others trying to build this -
I figured out the problem with the sound at this point. Having a 75 ohm resistor on L1 for the ground channel causes it to basically just not work. I end up getting a weird hollow sound. However, it is _not_ stable, as far as I can tell, with the 50 ohm ferrite from DigiKey. It blew up on me when I tried to switch back to the ferrite. Wonderful.
The other amp appears to be stable at gain 4 with the ferrites and caps on C3.
I swapped in an LM6172 again, with ferrite, not 75 ohm resistor as, again, I end up with weird sound if I have it there. It works correctly and very stable. It sounds rather good, very similar to the Hornet, which means it's aggressive and detailed, but the soundstage is slightly collapsed and it isn't as warm as my CMoy or something like an SR-71. It's also very quiet in terms of noise floor. When I first turned it on, I checked my power to make sure it was working as I couldn't hear anything (no pop, no hiss, etc.). When I played music through, though, it became apparent that it was working
It is running very stable now, though, with all ferrites on L1, caps installed on C3, AD8397/LM6172 combo. Neither chip gets hot driving my earphones or my friend's ATH-EM7. I may try removing C3 to see what happens, if it's making much of a performance hit, but somehow I'm doubting it is.
I'm going to order another couple AD8397 from AD, as someone pointed out to me that it's cheaper there and I am running out of money, but I have enough parts for another amplifier. Based on what I know now, I have some pretty solid ideas on how to build this successfully the first time around.
After this great ordeal, and considering my limited college student budget, I am accepting donations
If anyone has any questions, let me know (or if you want to donate

) and I'll try my best to answer.