First of all they don't live in mud puddles, but that has been addressed on this forum before.
The most important thing is the clean water and I'd also add a dash of aquarium salt. If you had access to blackwater extract, that will also help soothe them. If he is still struggling to get to the top I would lower the water a little more, and make sure he has something there to lie on near the top of the water so that he can just raise his head for air.
Don't be too concerned yet about him not eating. Sick animals rarely will eat. Even if he were not having problems it would not be unusual for a betta in a new home not to eat for days or even as much as a week.
Just be patient now and see what the clean water will do for him. If you do start to notice other issues, let us know and we will help in anyway we can. As you already know, BettaMomma is a wealth of information and helpful advice. She has gone through it all with her babies.
Just tell Twist to hang in there!!!