Wow, poor guy!
Unfortunately I don't know enough about betta care to know answers for you, but personally I would be worried about exposure to soap or other cleaning chemicals, as well as bacteria or maybe even fungus from that type of experience. But then maybe I'm over thinking.
I'll also say that I've heard that it can be risky using distilled water, but I believe that was *only* using distilled, not using it for a partial water change.
Please only take this as my own, newbie, knowledge, but I would be inclined to do regular water changes (not sure of percentage, 50 to 100%???) using conditioned tap water. Make sure he doesn't get chilled. And maybe add some aquarium salt???? I don't know.
Hopefully you should get some advice from the pros on the forum. I really wish you luck.