Serial number?
Under hydraulic stall (lift to top and hold, not tilt on this machine, as it may have chopper controlled hydraulics), what is the battery voltage? at rest, what is the battery voltage?
Can you confirm the park brake switch is in the correct position and connection state when the problem happens. the park brake on some of these has the function of cutting out considerable torque (but not RPM) to the drive motor (NOT cut out the drive, just no real torque to speak of).
have you checked for good (clean) no shorts to frame from -all- the power cables (not just the ones to the motor, but a check of all heat sinks and transistors/recs insulation)? Have you cleaned all the crud from the cables that run under the battery and replaced any cable that was cracked or swollen?
The foot control should have no effect whatever to the hydraulics cutting out, other than they both draw from the same battery.
have you gone through the "onboard diagnostics" with the "drs" switch to check the accel box and other inputs and outputs?
Consider a real good look at the seat switch linkage too, since an open seat switch may stop everything until it gets a good "SRO" (static return to off)
one more thing, let me get this straight, you are saying that after travel (is it the same if the drive wheels are off the ground? = less amps in the traction circuit.) there is no more hydraulic function, as if it went into lift lockout, is that correct?