Honestly I don't think the extra step is worth it since the VPS will still know your origin IP in the event of a subpoena anyway.

You could try https://privacy.com but ironically I doubt it'll help much in terms of privacy. (I use privacy for convenience, as it essentially mitigates your card numbers being leaked - they're locked to the vender and you can impose spending limits)

Unfortunately I doubt there's many people who want 100% privacy that you'd want as customers if you're a VPS provider. I know Vultr accepts crypto but you have to prove your identity first (still great if you're a crypto advocate as privacy isn't the only benefit).

Otherwise you're stuck with resellers and grey-market providers. You could try "bulletproof" hosts from various uh-greyhat-forums but trusting those is very mehhhhh.

VPS providers can log connections and you won't really know how long they retain the data until it matters.