"I have told" vs "I have been telling" (past participle or past continuous)?
This is tricky. Your a) sentence has the right meaning, but "been being" sounds so awful in English we never say it and find other ways to say the same thing. In this case, to keep your full meaning, the easiest way is to drop the passive voice:
"Although I've been telling everyone it was his fault for weeks, people have been asking me whose fault it was." OR "..., people have kept asking me..."
Notice I've also moved the "for weeks" part to the first clause because in this story both things have been happening for weeks.