Lunch Money, Beer Money, Sticks & Stones

I have all three sets.

I want to build a deck that will allow 4-6 players to use a deck that consists of at least one of each card from all three sets.

Mixing all three sets together doesn't seem to work as the gaming sessions seem to frequently have long runs of all attack cards only or all defense cards only. Also not getting grab cards for necessary combos was an issue.

Any recommendations for a custom deck using all three sets?