If bandwidth and space are not a problem for you, and you're only trying to work around an artificial limit on the number of files that your hosting allows, then there are some ways around that...

You could store the images (just the Imgur ones) as BLOBs in a database table, or pack them into a tar-like file format. Both of those approaches will require serving those images from behind a script (either to do a database lookup, or to seek to a specific offset and then read from the amalgamated file), but having them on their own URL (distinct from other TalkImg images) actually makes a lot of sense. That way, my earlier idea of modifying the image proxy to use a "substitutions table" simplifies to just mechanically translating the links on the fly (e.g. https://i.imgur.com/7wqVXzD.png -> https://talkimg.com/imgur.php?id=7wqVXzD, or something like that).

Actually, thinking about this more carefully, why even do this through TalkImg at all? Maybe it makes more sense to set up some dedicated hosting to serve those images without entangling them with TalkImg? I'm not sure who wants that challenge, but working on the problem in isolation will probably lower (and mostly fix) the costs, which might make it easier to find financial support.