Searching for an answer to this, I keep seeing claims that the Rumblepad 2 is supported natively.

Not as far as I can tell. I mean, it did start taking input from my Rumblepad after I tried running x360ce, but then it treated right on the d-pad as X, and none of my buttons work as a Y button. I have now reinstalled without putting in x360ce, but I'm getting the same symptoms.

Sadly, if I had done the due diligence to make sure this game would actually support my controller before I bought it, I'd still be in this fix. Apparently, it's supposed to just work.