Did you talk with Randal about your intentions to lead? Whenever I got the option to declare my rebellion, I without fail had that chat with Randal before that. Since he also is the one to come to your rescue, I assume getting him on your side is vital. (And it definitely works as an Iscari, though I didn't tried it with picking Heath as my mentor at the same time.)
I don't think I ever had that option and I visited the beach house every time I had the chance to because I knew as an Iscari it would hardest to gain rep there. Thanks for the suggestion though. Might try to play through again but I really don't think I missed it.