Tom,
Actually, I've been in a position similiar to what you described.
But, I was asked who I felt was the single person who made the most sense for the project. That made sense to me. I couldn't possibly imagine going through the process of seriously considering ten architects.
To be more reasonable, I'd recommend creating a short list, maybe 3-4 names.
I'd also second John MacMillan's comments. When someone says they don't care about money, I'd want to be sure they understand the very wide range of potential costs for the project. Unless, you are dealing with someone very wealthy, a difference of perhaps $25 million will probably mean something. At the very least, you would have to articulate what they will be getting for the extra money.
Assuming your question is not just academic, you may find yourself in an interesting position. There will be far more to discuss than just the choice of architects.
P.S. As your question hits too close to home, I can't give to my list.