Not sure what you're trying to say regarding back-dating. I think what you're missing is that long term holders of H1Bs universally have an approved PR or at least a pending one. That's the basis for extending it past the usual temporary limit. They need to stay on the work visa (with its limitations) until the immigrant visa becomes available (different from approval).

>seeking permanent residence on a tourist visa is not allowed, under most conditions.

In the US, it's allowed under your stated conditions. Immediate relatives of US citizens can generally adjust status to PR from any status (including tourist visa/visa waiver) or no status. Although if your underlying status expires you could be temporarily detained on a discretionary basis.

That said, it's better to pursue a K1 if you plan to get married shortly after arriving. It's very unlikely you will be granted a tourist visa if you tell the truth in the interview that you're engaged to someone in the US with immediate plans to marry.