A website that does both or would different websites work? BTC to Monero works really well on
ChangeNow or
SimpleSwap, just don't do anything stupid to trigger the system like visiting it with TOR or sending tainted coins. You can use a residential proxy for something like this.
It's best to stay away from anything associated with ChangeNow. They have a long history of unresolved scam cases, and your transactions may be frozen or your KYC request may be required for no reason. You can find a better list here --->
https://kycnot.me/ or post in this board:
https://bitcointalk.org/index.php?board=53.0 (you need to go first because of your trust).