I'll tell you my concerns.
the warmer the water you use, the more minerals are deposited. be aware of the condition of your water.
Sinks are often victim to a lot of biological and chemical deposits. You are always leaving traces of toothpaste, hairspray, and biological waste.
With that in mind you could achieve something more ideal if you used Cold water, and set up a heat lamp, some shade, and maybe deposit some perching and traversing stones. Only because the exercise your giving them is straining their muscles. slick and sticky surfaces wear and tear on a toads stumps, some plastics that are textured work better, but porcelain, ceramic, and glass would be something I would get my Netherlands kicked over.
I don't think you should push on their stomach. if anything lightly feel for something hard and solid, I'd worry about it's digestive tracks, they will gobble anything. seek medical assistance if this is the case. something to keep in mind when dealing with fake moss bark and rocks.
Honestly, it looks like your toad may have just gone into shock from handling and instantaneous changes in environment not understanding the surface he was walking on. It sounds more like he clammed up, because he wants to hide couldn't find cover, and felt hopeless. I can't say for sure, I hardly ever handle mine, I assume it's terrifying for them.
I'm also worried about the little guy. He's going to get eaten. You should build them two proper and separate containers or divide one. get some top coverage, and things to hide in, and under.