I've started the sorting process, and here's how the incongruities will play out:
In the case of two or more teams on a card, these will be randomed off amongst those teams. If it comes down to a player on a team claimed by a break participant and a player for an unclaimed team (my de facto teams), the participant will automatically get the card.
Players depicted as collegians will go to the pro team they were first part of (though not necessarily the first team for which they played).
Minor leaguers will go to the big league club for whom their team is an affiliate.
If a player is listed in text as playing for one team, but is pictured in the uniform of another team, the card will go to the uniformed team.
Franchise lineage will be followed (i.e. Expos ---> Nationals).
Complaints may be submitted in the comments section of this post.