We're working towards accepting cash by mail in a month or two, and regarding cryptocurrencies, we've been trying to reach out to proxysto.re unsuccessfully for that. If you know of a similar option, we'd love to hear about it!
If the goal truly is privacy, and that's why you're adding cryptocurrency options, then adding a middleman like "proxysto.re" or any other, then you're not giving users the privacy you say you want to give. You really need to handle that on your end, if that's something you want to offer for the purpose of privacy.
Take a look at how Mullvad implemented it, which I guess is where you got the "cash in a letter" method from, they also handle cryptocurrencies by themselves for exactly this reason, there is no way for you to actually be able to fulfill the privacy promise otherwise.
Privacy Pass would also be a good option. You can use it with Kagi, where you’ll have cryptographic tokens that you can use for searches without them being linked to your account. Even if you use a non-anonymous payment method, you could still use the service without leaving a trace.
I have to agree with embedding-shape, don't use a middleman please. Just accept monero payments yourself <3
Once you accept Monero I'll give it a try :)
Taler could be a good match: it's a digital coin that has been in development for a long time and is currently starting to see real use. It guarantees the anonymity of the buyer but not the merchant (to avoid tax evasion and money laundering). It's not a cryptocurrency (no blockchain, no intrinsic value with floating rate), it's really a digital form of whatever currency your exchange uses.
Now the only working exchange I know is in Switzerland (https://taler-ops.ch/en/). I wonder if you could legally use that from another country... I think GLS Bank is also supposed to have an exchange running in Germany some time this year but there have been delays in the past. Anyway it's probably still a bit early but it could be something to consider.