only 3 Tons for 3700 Sf Ft?
Depending on how well your house is built, meaning insulation, thermal mass, air leakage, window locations, etc, etc. as you can see many things factor into calculating HVAC, guys who 'guess' based on square footage are usually wrong. If this guy has done his heatloss/heatgain calcs and has good references than I would say his work is accurate at 3 tons. The zoning really helps since the AC is primarily for the top floor, secondary on the main floor and redundent in the basement, and reverse it all for the heating in the winter. Zone systems are a great way to go and give you more flexibility in heating/cooling your new house. FWIW have an independent engineer verify his work, might well be worth a couple hundred bucks.
And for Flyby, that's a alot of cooling, what are you building your house with, or should I say without!! I've built small commercial units that size with less than half that cooling, something doesn't make sense unless your version of mid-south is Death Valley, CA.