Great question! I've heard that in-person cash exchange is your best bet, if you're wanting to be completely off the grid. There are services out there that can help with the exchange (early in Bitcoin, there was an escrow service in which you deposited cash into a savings account through an ATM, and an anonymous wallet would be credited with the appropriate Bitcoin). Not sure where that stands now.

Oh! But to your question: Mullvad VPN seems to be highly regarded, and has an option to configure a recurring payment that they (claim to) decouple from your identity. Their service even supports defining multi-hop routes.

And to be clear: My goal is to obfuscate my identity from malicious individuals (think: politician that wants to be kinky, but has to resort to online interactions during COVID lockdown, and wants to avoid both simple tracert IP identification as well as a potential password breach & leak of social media platform X). Hiding my identity from governments is not my goal, so trusting Mullvad was an acceptable risk assessment. I'd add additional layers if I wanted to be more anonymous.

My next step, when I get around to it, is to try to track down a cheap anonymous virtual host to SSL into... then at least I'll have a static IP. But I'd still be up a creek if they ever wanted to do two factor for some reason.

You can buy Monero instead, and funnel it through xmr.to to pay in Bitcoins. Another alternative might be fixedfloat.com. Tested both, but you had better not exchange big amounts.