"That's going to be REAL popular. Asking the whole board for all their personal details. "
Absolutely not required, and in most cases, should not be done. Ask them to register (and manage) their own data, then provide the ID. Keeps the person from handling the entity aspect from having to take on managing each individual and allows the individual to enter data as they see fit.
In my own case, I could have done it since I know all the data, but it is not my place to determine what information each person wants to make public. The side, and actually important bene is it is up to them to manage their own data should it ever change. I assume the data will eventually leak to the dark web, if not to a public site (just as it would be foolish to consider one's SSN private). I do not want to worry about more than my own personal data.