Ahh, then this is a clear problem - the dehumidification function and capacity of the air units must be addressed. Also building air leakage. The fundamental design and control issue of a radiant cooling system of any kind is to CONTROL THE DEWPOINT. The lower the ambient dewpoint, the lower you can drive the radiant cooling temps to get more cooling capacity. The Air units in this case must also have a dehumidification sequence to insure a controlled dewpoint.
From what you've described, the operators should NOT have tried to use the radiant floor cooling to "get" more capacity unless they first addressed the dehumidification function of the air unit(s). Also, given that there is at least 2 cfm/SF worth of air circulation, was there not enough cooling capacity in the air side? Should have been, if it was designed properly.
Normally with radiant slab systems of any flavour, they are supposed to be used for "steady state" operation- set the slab to temperature X and control that from a slab temperature sensor feedback, and use a constant flow, variable temperature circulation system. When one gets high transient thermal loads in the space, ALWAYS use the air system as the "first responder". Use the radiant cooling only if you can dehumidify low enough to allow lower radiant cooling surface temps to try to get additional cooling capacity.