What type of system are you planing? Sounds like it might be a combination drip, and water culture system. Also you mentioned using 56-quart containers, are these containers short and flat or taller and less wide? Also were you considering all three plants in one container, or each plant having it's own container?

Depending on the setup and design, one benefit to using baskets that hold more growing medium is the more growing medium the better water retention to the main root ball. The more growing medium the more water it can hold, this also depends on what type of growing medium you use. A downside to using smaller baskets for large plants, is that large plants have large root systems, small baskets might choke the larger roots of the main root ball.

I have grown tomatoes in both 2" and 3" net pots.
You don't need anything larger than a 2" net pot

This was my system from a few years ago. of the four, 2" net pots, two had two plants in each. I never had any problems with root congestion. once the roots get through the pot, everything just dangles below.