It looks like imgur has an
api, but it doesn't look like the API can retrieve images currently. Perhaps they may be willing to add such functionality.
The link of the image IS the image, it doesn't make sense to have an "API" for that. The only solution is imgur flexibilizing rate limiting (and that's not even a complete solution, since the forum usage can outgrow the limit) or whitelisting the forum's proxy IP. I don't think neither are going to happen.