Those 22 House members should have held out for a Republican war room with an emphasis on messaging --- both for external consumption and caucas unity.
Having a uniform answer to why a shutdown, what it means, what it will take to avoid it and the short and long term benefits would go a long way in giving a spinal infusion to those members needing one --- regardless of why it's needed.
I'm not exactly sure what you mean with that. There is, and was, no way to force every member of the caucus to support every shutdown. And any shutdown that does start getting discussed is going to be very fact-specific, so it'll have to be discussed/negotiated when and if specific terms for the shutdown are raised.
The concept of "caucus unity" evaporated day one anyway, when the individual members of the Freedom Caucus used their power to stop the majority of the caucus from electing the Speaker.. The more moderate members of the caucus likely already feel they've made every concession they're willing to make. And the Speaker being in a "straightjacket" means he's not going to have the leverage to make them do otherwise.
That's the flip side of "empowering every member".
For instance, neither Social Security nor SSI checks stop during a shutdown... something even Republicans get wrong.
They don't stop during a failure to approve budgets or appropriations. But they will eventually stop if the debt ceiling isn't raised.