To dream the impossible dream....
A tank of sedated bettas, going on for years and years - are you sure that's what you would want? It sounds like a nightmare scenario to me - a half life for no other reason but human whims.
Plus it might be hard to maintain.
However, if you get one pair of Bettas, you can breed them. Raise the fry away from the parents in a large tank, and remove the females as soon as you can. Once you have reduced to population to about one male per 25cm square on the surface area (large low tanks work) they will find a zone. Finnage will be damaged in border disputes, but with floating plants, the males will defend their stations and no one should get killed. If you can start with a less aggressive plakat group, you won't even have shredded fins.
I have had similar, small scale set ups with wild caught Betta splendens, or fry from them to be more precise. It really needs a tank with a large surface area. I also bred plakats and gave the young to a friend who had built himself a shallow tank the size of a dining room table, which he placed under a window so he could grow Pistia all over the surface. He had a great time with the tank. It was a very unorthodox looking thing, but was a very unorthodox project to begin with. He replaced a colony of long fins with my pla-kat because he wanted a more natural set up, but he said as long as you never added another fish, it worked. If a fish died, the territories of neighbours expanded. But he felt that familiarity from a very young age allowed the balance, and any change meant another territorial squabble with resulting injuries. hefelt that if you bought a bunch of Bettas and put them together in the tank, deaths would result.
I watched the tank a couple of times and it was too static for me. Each male just hovered in his territory, looking up for bugs. The guy fed them fruit flies so there would be no rush to food (and no reset on territory). He sprinkled them on the surface carefully. The Bettas only moved in narrow areas, and not much.
He was a very OCD kind of guy, in the entire house as well as in his aquarium choices, and I'm not sure how many people would want that set up.