If I may make a suggestion, perhaps you should spread out the packs more. I think part of the reason he gets burnt out is he gets sent packs of like 20 games every week and he has to go through all 20 all at once. If he instead did packs of say, 10 games every week or every other week, it might alleviate the burn out even if it takes longer to get through. This would also allow room for him to get addicted to a particular game for 20 minutes and still avoid shafting other games.
Considering that the only "prize" for these jams is getting shown on stream for 5 minutes, I think we should look for solutions to include as many games as possible rather than start excluding them. Just my thoughts.