Is there any non US-based payment processor that is known to be friendly towards this setup? I am based in EU and the project is perfectly legal and has nothing to do with risky businesses like porn industry, gambling or anything like that.
Banks in the US are legally obligated to *not* just take your word for this.
KYC (Know Your Customer) laws attempt to eliminate anonymity in fund transfers which sounds like what you are really looking for.
How do you prevent that A use a stolen credit card to sends money to your service, and then extracts the money?