It worked like a charm.
I bought a tub large enough for the statue, and 4 gallons of Super Clean. I tested the Super Clean on the base of one of the statue's feet and there was no resin damage, so I put it in the tube and covered it with Super Clean.
After 20 minutes, there was a DRASTIC change, almost all of the paint had loosened. I used gloves and a toothbrush and began to gently scrub at the paint.
I let it soak for 2 hours and about 98% of the paint was gone. I let it dry overnight.
This is my first statue, so I don't know if this is normal. I found tons of tiny resin "balls" all over the statue. These were easily removed with a pick, and I used ultrafine sandpaper to smooth out rough edges. I then primed it with Duplicolor sandable filler primer.
Painting has begun, I'll update again when I'm finished.