I don't know if you can get some, but when I was doing research for my thesis with fathead minnows, I had to anesthetize them using MS-222 or Tricaine Methanesulfonate (sometimes marketed as Finquel). Apparently this anesthetic is safe to use in leopard frogs as well. I'm not sure how pacman frog physiology compares, but I think the stuff is safe (in the proper dosage) for any cold-blooded critter. You basically mix up the solution in water, plunk them in the stuff, wait for them to fall asleep and then you are good to go. My minnows needed a solution of 185 micrograms/Litre while leopard frogs are usually dosed at 200 mg/L or less. It's a big risk, but if you've exhausted ALL other options, this might be a last-ditch effort...

Another possibility might be to massage it out? I know of someone who's axolotl swallowed some rocks that couldn't pass. The vet said surgery was not a viable option because of the damage it would cause. Likely the axie would not recover and so they were sent home. The person massaged the axolotl's belly to force the rocks upward. When the rocks were in view, they were able to reach in and pull them out.

This is a really sad situation and I really really hope Cody recovers!! My thoughts and prayers are with you!! Good luck!