I would think Bt would do the trick, just apply it as directed. If they are inside the paddles, maybe you should remove & dispose of the affected ones.

Are those reddish things the caterpillars? Can you pick them off & destroy them?

http://entnemdept.ufl.edu/creatures/bfly/cactus_moth.htm

From the page:
"Please Help! We would like to hear from you if you know of infestations in your area or if you know of the location of Opuntia cactus stands that we could check, particularly if the sites are inland or in front of the leading edge. Please contact: Dr. Stephen Hight, Phone: 850-656-9870 x 18."

Yes the red things are the cats and I cut all the pads that were infestated off put them in a bucket then poured boiling water in the bucket. That should be the end of those but the moths could lay more. Sad because they are a new evasive. Never had a problem till now. Prickly pear has always been a very low maintenance plant.

I handpick/smash most of the caterpillars and other insects that prey on my plants. It's the simplest and most effective method IMO. Also the least harmful to predators/beneficials.

Neem oil and hand picking?

Neem seams to have no effect on them at all

I had them years ago in my paddle cacti (opuntia rosa i think was the variety) here in s.w. Florida. I tried to fight the fight and would not just remove the infested paddle but cut it open and kill every worm in it. But they won the war and i no longer have paddle cacti.

Pea, I'm sorry to hear that.