Two years sounds like a sufficient buffer period to me. That is eliminate any books actually selected by the other club as the book of the month during the previous two years. Given some of the categories of the other club I can't think we are talking about eliminating many books from consideration.
As far as the other question that came up, or maybe it really didn't?
I say stick with the procedure first outlined. A person is selected at random. This person selects one
book. There is an essentially an up or down vote on this book to answer only the question is it literary? Yes, the book is selected. No go to plan B.
I am looking forward to A Passage to India
. I've never read it, but did read The Jewel in the Crown
last year and I am interested in another author's perspective on the same place and period.