Variable speed motor controllers for single phase are either really,
REALLY, expensive or they don't work very well. They also have many different requirements like specific motor types as you are noting.
What kind of motor you have should be specified on the motor's name plate.
Most of those fan controllers are not good for more than about 3/4hp.
PSC motors have a single cap. If yours has two caps then it is a capacitor start motor.
The biggest issue with variable speed on a single phase motor is that single phase motors have centrifugal start switches. So if you externally turn down the speed below ~70% you can get the start switch to re-close which will toast the motor in about 3 seconds.
Why can't you use the various valves they provide to route the flow to say your foot outlet away from the back outlet that's bothering you?
If that won't work then you should consider replacing the existing motor with a three phase motor and getting a micro VFD to run it any way you like off of single phase. Motors come with standard case types and dimensions. Finding a three phase equivalent motor to a single phase 1-1/2hp motor is very easy.
Otherwise put in a bypass valve to shunt back some amount of water from the pump outlet to the inlet to reduce the delivered amount. Don't bypass more than about 70% or you may have pump heating problems.
A final point. The water heaters in most hot tubs are grossly over sized to heat all that water up from cold water in a reasonable amount of time. You need to check that if you slow-the-flow, it doesn't reduce the cooling ability of the water flowing across the elements to a point that either over heats the heater, or somehow puts out scalding water into the people space.
Keith Cress
kcress -