BTCPay is what you are looking for despite its name, but be sure to read their documentation to see how to compile extensions that provide support for each altcoin or you could hire someone to write one for you in case one doesn't exist for a particular coin.
You can also hire someone to manage the hosting for you themselves because third-party services may have some strings attached (not all countries supported, limits, verification requirement, and so on).
Yes, I discovered this site during my research and it is on my list of possible solutions.