@argv_minus_one @aral I also don't see how maintaining a dynamic site would be feasible, both cost-wise and security-wise.
I think the most practical way would be to convert your website to a static one, if content is what you want to preserve. Virtually any web server setup supports serving static files from a public directory (or can be set up to do so), so you can just dump archived pages to a subdirectory and add a redirect to there. Since they're static files, a simple 301/302 would suffice.
That requires being in control of both the domain you're migrating from and your new server configuration. So yeah, this won't help if you're moving from a *.wix.com site or to somewhere where you cannot add redirect rules.