What exactly is needed to run such a service? honestly if both wallets are completely open source, then there is no need to point fingers and have such dramas, one could simply fork the wallet and start a new service, a better one.
At bare minimum, a server and ability to follow guide about setting either coinjoin software. But gaining people's trust and liquidity to perform CoinJoin isn't simple.
In any of these 2 cases though, you'll still be running a centralized service. As a coordinator, authorities will be able to pressure you into shutting down, implementing privacy-breaking changes and helping them deanonymizing users through blockchain analysis. Maybe they'll force you to partner with a blockchain analysis firm, even. Does some of this sound familiar?
One solution would be to switch to decentralized approaches, such as
JoinMarket.