Does a book of 3's in Hand and Foot work?
Assuming you're playing with the Red (100) Black (5) variation (there are not official rules for hand and foot), then the purpose of the 3's is to add a bit of randomness to the game to offset player ability.  If your goal is to remove this randomness, then you can simply treat all 3's as normal cards and the game will 'work' just fine.   I have played that particular variation.

I'm not sure by which rules you're playing, but if you're allowing threes to hit the table singly, and also allowing the bonus for making a book of them, it's a bit of an unfair advantage to that random chance.

Pagat - Rules to Hand and Foot