Male Betta can, in certain circumstance, live quite peacefully with other fish. It all depends on the temperament of the fish in question. Since you have no real alternatives, there is no harm in attempting to place him in the 29 gallon, watch how it goes, and remove him if there are problems. If the fungus is cured, there is no real risk in placing him in the tank, and the fungus will be less likely to return in the larger community tank in my opinion. I currently have a relatively aggressive female in with 10 neons, with no problem. If there are problems, you can do a non filtered environment.
I usually never recommend a non filtered environment as they are difficult to maintain, but in this case I will make an exception considering you are already well versed in fish care.
Find and choose at least a three gallon bowl, one that is longer and squat, than it is high and round. Choose a flat pad heater that sits underneath the bowl to keep it relatively warm. In an aquarium the optimal temperature is around 80 degrees, but that won't be possible in a bowl. Staying at or very near 78, as long as it is constant, will be fine. Regular monitoring with a thermometer is very important.
The key to keeping an unfiltered Betta habitat, is DAILY water changes. The once a week system of a regular aquarium just will not work for an unfiltered bowl. 1/3 daily water changes with dechlorinated water will keep the water fresh, and aerated without the need for filtration. Remove uneaten food and detritus at the bottom immediately.
Never use live bamboo, it is -not- an actual water plant, and is the main cause of fungus in a bowl habitat due to its breaking down. Instead use silk plants for the Betta to hide in, and avoid decorations that simply displace water and take up room in the bowl. You want him to have as much moving room as possible.
Pinch of aquarium salt. Not the "dose" recommended on the box, its too high for a bowl situation. But one pinch in one of the water changes once a week will help inhibit the growth of fungus and bacteria that could harm your fish.
Hope this helps.
2 10 gallon tanks, 1 20 gallon tank, 1 Fluval Edge, 1 29 gallon tank, and one backyard pond.