A. Alignment.

Find experts whose intentions *already* align with yours. Minimize the need to convince anyone of anything.

B. Ego

Appeal to how awesome they are, what a contribution they will make, how big they are and how they will have such a huge impact on your idea.

C. Involvement

Show them how their involvement in your idea will noticeably impact the progression of their own goals (which, as above, should be aligned with yours.)

Notice something? You have to SELL. This is still a sales job. You can pre-qualify to make the job easier, but there still has to be a good sense of exchange for their time. Nobody wants to sit on a board that does nothing.