Yup, Monero is probably the best option. I've heard good things about Z-cash, and Bitcoin can work on the lightning network.

Then I guess I don't understand your problem.

Payment processors like Visa and Mastercard control a huge chunk of the market, which gives them a lot of say in what transactions are allowed. Even if you avoid credit, most debit cards go through those two companies, so they can restrict what transactions you can make.

With cryptocurrencies, there's no restriction at the point of sale. Your problem seems to be that converting crypto to fiat could be problematic, and they'd potentially be stuck with "useless" currency. My point is that's a much easier problem to solve:

• if their exchange stops converting a given currency, they can convert to one they do accept
• if their exchange bans their account (e.g. due to the nature of their business), they can switch exchanges
• there are ATMs that dispense cash for crypto
• if no exchange will work with them, they can make direct exchanges with regular people (i.e. "launder" the money)
• they can also spend the currency directly

There are a ton of options to convert crypto to fiat, there are far fewer to select a different fiat payment processor.