Yep, I'm another one who can't get into the hearings. None of the solutions I've read work for me.
I started a game with v1.05 (GOG), playing a mindless soulless rampaging murderer, slaughtering everyone I see without speaking to them, and doing as few quests as possible. I cleared out the three houses before even confronting Webb. (And found the one person I'm not allowed to mindlessly slaughter.)
My quest log says I need to tell Lady Webb that I'm unable to get an invitation to the hearings, but Webb says she's a last resort and won't invite me herself. Patching to 1.06 didn't help. I need the "burned all bridges" option to appear. Is there a console command that will do this?