Update on my experience with these worms. I removed the dish of uneaten worms from the other tank yesterday. I didn't think any of them had been eaten, but it looks like I was wrong about that. I just found one of them sliming its way around on the glass near the top of the tank, very close to where one of the little frogs was hanging out.
The only way I can imagine it could have gotten there is if the frog pooped it ou alive. These worms are not slimy (unless they've passed through a digestive tract), and they couldn't even crawl out of the tiny glass dishes they were in, let alone climb up to the top of the tank.
I'm really pretty grossed out right now.
I'm glad things seem to have gone better with your frogs.