You probably want to look into some kind of filter (I'm guessing maybe you don't have one since you are doing complete water changes). A Whisper 3i is good for your size tank, and it doesn't create enough turbidity to disturb the bettas. It does run on an enternal air pump, which can be annoying to have to set somewhere. Bettas in bowls or tanks without filtration do tend to look worse off (the ones in the cups at the store make me sad), so doing that will perk them up in a few weeks once the filter establishes. If you get a Whisper 3i, buy a Fluval sponge and cut it to size to fit into the little box (don't replace it, just rinse it lightly). Replacing the carbon will just ruin any progress on your biological filtration, and you'll save some money too.
*Edit: The soap isn't wrong by any means. I don't use it, and I think you'll find that most people don't either. That's mainly just laziness, paranoia about getting any contaminate into the water, and mainly the fact that with anything above a 2.5 gallon pretty much everyone only does a partial water change because its impractical and unecessary to do a full one. If you do use a filter, go with partial water changes. I would say you are going the right thing doing full ones with your bettas right now though.