Well, that solved it for me anyway by using your notion of "highest number of matching conditions".
What I did was use the default screen for my "rebuy period" screen set.
Pretourney screen I just add the condition of "before game" and buy-ins and add-ons allowed = yes.
Then, for "post tourney" I set a bunch of conditions - that it was buy-in allowed, but buy-ins = over, add-ons allowed, but add-ons = over (I kind of can assume that the tourney won't end before the end of buy-ins), and made the tourney type "no limit", and made players remaining = <3 (because of course there will be less than 3 at the end of the tourney).
For my "no-rebuys" screen set, I just set the condition to any stage and rebuys and add-ons are allowed, but are "over"
Then everything works as it should. Pre-tourney screens show up before the tourney starts, the default displays during rebuy, the "no rebuys" screen sets show up after my round 4 when it should, and then when I bust out the last player my "post tourney" screen sets show up.
Thanks Corey. Not really a bug, just needed to make the conditions work for the software parameters.
Peter