Where can I pay professional researchers online to verify my results and answer my questions?
The harsh answer: You probably can't. At least, unless you are somehow quite wealthy, and if that was the case, I suppose you could simply pay for enrollment at another university. Let me try and clarify a bit.
As a researcher I get many requests from people who want me to look at their particular problem. This ranges from

Fellow researchers who want to discuss - I most often oblige (at least if I have time, and their request is interesting or relevant).
Students who I don't know in advance, who wants guidance - I help if their question is well researched and not too polemically phrased.
Students from my own institution, not under my supervision - I always help, as this is my job.
Amateurs who have invented the a new method or theory for something, and wants it checked - I rarely do more than skim it.
etc. etc. etc.

You are in the last category. If you are to convince me that I should prioritize your request over the others, then I should be immediately convinced that your idea is really something special. My field is not mathematics, so I can't tell here. But judging from comments from professional mathematicians, neither can they. The second option you mention is money, and this is where I think you need to be fairly rich. If a purely monetary argument should convince me to push you to the top of the stack, you would need to pay me the equivalent of my going rate when doing freelance work, around 200 €/hour.
My best bet is to either:

Try and get re-enrolled into a university. There people get paid to answer your questions.
Try and find someone who would be really interested in your specific problem, and write them.
Undo whatever you did to get banned at math stackexchange, and try again there. Being nice gets you a long way, being polemic and insisting that only a professor can answer your question, will get you few friends.