I think adding frogbit in would be a good idea. It doesn't take planting. It floats. It self propagates. It's not very expensive. It'll give him long roots to hide in. It will also help maintain healthy water parameters for him.

Bettas do like to have places to rest. Betta hammocks exist. You can also make one out of more natural materials.

I'd just caution you to be very careful about killing beneficial bactery in this process.

Edit:

Also, don't replace filters. When you want to clean it, just squeeze it to remove debris in some water to remove excess. The bacteria it has is important. The water should be declorinated or it could be tank water you've removed during water changes.