I think your last two sentences firmly sum up the situation - although I thoroughly read your entire post, of course. The organization is asking a lot from its volunteers, IMO.

Perhaps let the organization know that while you appreciate their cause - the volunteer services they need are not a good fit for you. Or, if there are volunteer duties there that are acceptable - perhaps trying reiterating one more time what you are wiling to do and NOT do.

Boundaries are tough! I'm working on them, too. It's hard to say no but its OK and it's not selfish. xoxo