I have one of those subs that I picked up from Frys so many years ago. Sits around collecting dust

Last time I had it running, tho, I don't remember any hum problems. Altho, the auto-turn on always seemed a bit sketchy.
More to your point, tho....
I also have a Klipsch KSW-150 (150W, 10") sub. I've had that sub for 20+(?) years now. Some years ago I ran into a "skritching" noise that made me wonder if the subwoofer voice coil was falling apart. After careful diagnostics, I determined it was a solder joint on/near one of the op amps that had gone cold. Fixed that and then a year or 2 later the sub developed a hum. 1st I thought it was coming thru the LFE channel. Not so. Soldered the P/S filter caps. While I had the amp out, I also resoldered all the other connections of components in the main P/S section. The sub has been doing great ever since.
Moral of the story....if it's AC/60 Hz hum, that usually means something in the P/S. The only other possibility is a cold solder joint on the ground of another component. However, if that were the case, the issues may be different, or worse, than AC hum.
Since you have a bulging cap, that would be my 1st suspect. Since you're going to be in there replacing the cap, I would also suggest that you go thru the rest of the supply section and resolder everything, just to be sure.
BTW - Just because a cap measures the "right" capacitance, the ESR (Effective Series Resistance) might be too high to continue any further effective filtering.
Don't know if it helps but I attached the schematics for a KLH ASW10-120 Power Amp and P/S section. May have serious differences from the ASW80-80 but it may be similar enough in the P/S section to provide some help.
Good luck.....