IANAL. Can non-citizens run US-based companies? If yes, can't this be done through a company, then OP would just be forbidden from drawing a salary from this entity?
Only if they want to get paid in any way, right? Can a person run their company w/o drawing any profits (i.e. no W-2 needed) and not have to go through the visa process? If I were to look for a way out of the situation ("I want people to pay so that I have money to maintain the infrastructure"), this is how I'd try to approach it ("create an entity that is allowed to accept money from other sources and use that money only to run the infrastructure").