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

Monero is perhaps the best option imo. Here's the official page about it, but basically:

• not profitable to mine, so most miners are enthusiasts who want the coin to succeed
• privacy-focused - basically creates a ton of fake transactions to mislead snoopers
• relatively popular - seems to be the most popular coin recommended by privacy enthusiasts (e.g. Mental Outlaw, he even gives a discount on his store for Monero)
• not popular among speculators - they mostly stick to the big ones (BTC and ETH), as well as new startup coins
• low cost transactions, fairly short transaction window

It's far from ubiquitous, but it's popular enough that if a place accepts any crypto, there's a good chance they accept Monero as well.

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.