Another alternative: Use a Rizful.com node with a VPN, and delete the node when you stop using it.
The biggest limitation of using lnproxy as a tool to receive payments to your own node privately, was the fact that the relay would learn your node id.
If you run LND, the issue is now solved: the latest version of lnproxy supports blinded paths. Try it today.
https://github.com/lnproxy/lnproxy-relay/commit/f5670e7dc23ff95e37453a39985b80983c2b9ca6
Discussion
Yes, spinning up new nodes for privacy is a very good option. Better in lots of ways. But requires onchain transactions so could get expensive.
Yeah, it does matter what the current fee rates are. Recently fees have been pretty low though, so you can pretty cheaply get inbound liquidity from Rizful.