TG forfeited in Chicago last year on Sunday, Premier dropped out of the AA World the night before the tournament, then the combined Premier/TG forfeited in St Louis, and now forfeited at the Dudley.
At some point this is a team that should be expecting to make it to Sunday.
As far as limiting teams, now you are asking directors to go further in the hole than they already are. I'm not sure that is viable.
Possibly starting earlier on Friday is something that should be discussed.