How long had the battery been off the charger and being used? also, we need to be able to read 1/10 volts to be able to do the math correctly.
If this is a freshly charged battery, you have battery problems. if this is a battery that has ran for 4 hours, then it is not -all- that bad, but not "good", either.
Reading voltage during acceleration is worthless, and *dangerous*, it can change based on the load of the drive motor (level floor, amount of pedal, speed already reached when reading) as well as the fact you may be reading currents that are not from the battery, but generated in the controller (some controllers have 2x battery voltage in some areas, because of the electronics).
The acceleration is controlled initially by a variable resistor (potentiometer) attached to the accelerator pedal, (accel pot) but is also adjustable for fine tuning within the controller's logics. your problem may well be in the traction controller, the accel pot, the linkage, or the wiring.
There are a few types of 'speeds' in an electric truck, (creep, current limit, controlled acceleration, 1a time, 1a drop-out) and they work together, so an adjustment of 1 may affect other settings, and these things often require a special handset to adjust, and special training to safely adjust (and your forklift is not safe to operate the way it is now)