@pfaffman’s assumption that it wasn’t possible to use Codeforces as an auth provider was correct. Codeforces is basically maintained by one guy and I doubt he would implement anything for something that is still in the planning/funding phase.
I agree that polling is suboptimal! That is why the proposed solution of querying it when the user logs in seems to be a good balance between [user’s interest of] consistency and not hitting Codeforces’ servers enough to call attention and possibly being blocked off.
If our specific case for the Brazilian community is successful and other communities try to do the same, maybe Mike (the one guy responsible for Codeforces) will implement something like this.
Nonetheless, thank you very much for the suggestions! I will keep them in mind for the next time I meet Mike in June next year when I can try to convince him about helping out and possibly optimize whichever solution our forum might be using by then.