One solution is a traditional webmail provider being willing to reuse that primary user domain for forwarding addresses. There are two that I know of doing this, Fastmail with @fastmail.com and Apple with @icloud.com. These domains probably won’t ever be blacklisted, because you’d also blacklist a ton of primary email addresses. (Aliases, which most providers have, tend to be too inconvenient and quantity limited.)
Another solution is to use different addresses at your own domain, which trades anonymity against the company you sign up with for freedom to change providers.
I think all three of these, including announced proxies like MPR, can be the best solution depending on whether you just want to be able to cut contact or you want privacy, and from whom.