I'm a little bit worse situation! my fingerprints were rejected in september, and now I'm waiting that the FBI process a new set of fingerprints.
In specific for your questions, in my experience, I would say:
2) Provide another LoE instead of FBI PCC?
I tried this with police of the city of NY, and CIC answered saying that they need the FBI PCC, no any other one, so, don't waste time and money trying to get that.
He meant letter of explanation for the extention, not another local pcc from state level..and you are right about local PCC
3) Is the second deadline prolongation possible???
Second extention is completily possible, they understand that the process at FBI could take more time than they give.
Hope this helps!