I read the first 2 pages, then skipped ahead to page 6 so sorry if I missed anything.
My 2 cents would be to ask the group what to do.
When the cheater is not there, talk to the group: "Hey everyone, I have to break some bad news to everyone but "john doe" has been observed manipulating the deck on more than one occasion, and it's been confirmed by someone else. There's no question if he's doing this, he's doing it. I am planning to not invite him back, but as a group, how would everyone like to deal with it?"
Then follow through with the decision.
My 2 cents would be to ask the group what to do.
When the cheater is not there, talk to the group: "Hey everyone, I have to break some bad news to everyone but "john doe" has been observed manipulating the deck on more than one occasion, and it's been confirmed by someone else. There's no question if he's doing this, he's doing it. I am planning to not invite him back, but as a group, how would everyone like to deal with it?"
Then follow through with the decision.