This answer probably isnt much help, but on some heavy equipment, such as mills and pressure vessels with variable inventory, we use load cells with reasonable success.The cell is normally just a strain gauge fastened to an appropriately dimensioned strain member.
On some of the hydro turbines I work on, we use thrust bearing oil jacking systems, which show a residual pressure
while running. It would take some pretty fancy math to deduce the thrust, however. Probably next to impossible with any reasonable level of accuracy.
If you are after temporary readings, the humble portapower cylinder and pressure gauge may be of some use, as the loads you are looking at arent especially high. With a little vibration to break stiction, the pressure X area gives reasonable accuracy. You can calibrate against a test load, and check against the pump deadweight. Obviously you will have to deduct in-service clamping loads, which may have an unacceptable effect on accuracy.
If the pump is mounted on a full contact bedplate, I dunno.
Perhaps remote anchored dial gauges and testweight(s) with assumed stiffness characteristic.
Whats wrong with pressure times discharge area, or are you looking for a transient?
Sorry about the woffle; may encourage a more coherent response.
Cheers
Steve