I've built something similar https://richie.stormconcept.de [0], but the proxying is what amazes me:

How do you proxy the requests?

I think it's a great idea and incredibly useful.

[0]: uploaded it to https://github.com/samuelantonioli/richie (added "expires", good idea)

p.s.: I've solved the problem with fixed headers using a fixed header with a high z-index (unfortunately this hides the fixed header of the copied website).

p.p.s.: Maybe it's possible to build it as a small community-maintained project, that would be great.