You know, this would be a fantastic time for Google to get their sandbox in order. If we need to do it like this, go ahead and create a secondary user, call it sandbox and let me install all my wild and unapproved apps there. SecureNet can automatically fail in Sandbox. But I don't think they're going to do that, ultimately users who actually care about this are an absolute tiny percentage of the market. And weirdos…
I haven't tested it myself, but as far as I know you can run ADB in the phone itself via Termux. Perhaps it's possible to make a wrapper that install apps from F-Droid with ADB? It would mean that you would only need to be tethered to the your PC once. Obviously they'll eventually remove this because Google is hostile to things like ReVanced / some spook wants this power.
I'm definitely not 100% sure about that though, so someone please correct me if not.