I believe you are overstating the current requirement of those valves. One thing that is helpful, is that the valve 'operator' is a simple resistance heater, as opposed to a solenoid, which draws more current than its wattage indicates (which is why both solenoids and supply transformers are given 'VA' ratings, rather than simple watts and amps)
Just for grins, I run the 800-foot maximum of run for number 14 zone wire through a calculator, and it returns as 2 ohms, which calculates to just about 2 amps maximum of valve draw. That raises the possibility that a controller capable of powering at least 3 modern solenoids per zone might be capable of operating those Thermal Hydraulic valves. I would be looking for any controller with a large (50 VA minimum) power supply transformer, and that rules out even the good entry-level models.
What was the original controller? What did you install to replace it?