First up, if you are expecting the controls on a wheel loader to perform like those on an excavator I think you're going to be disappointed. The different uses for which the two machines are designed means that the loader controls are never likely to have the same level of fine control as an excavator.
If I press the button, which is supposed to slow down the hydraulics and give more control, it seems like I have to move the stick a long way before anything happens,
Which "button" exactly are you talking about.? Can you post a photo.? (You may have to make a minimum of 3 posts before are allowed to upload photos)
Everything I can see regarding speed control in the Operation & Maintenance Manual refers to ground speed not hydraulic implement speed, but maybe I'm missing something.
You do have an O&M Manual I hope.?
Sorry to be the bearer of bad tidings but unfortunately the only way to calibrate the joystick position sensors and the proportional solenoids for the implement control valve is by using Cat ET. TBH a re-cal is the first thing I would suggest because who knows when they were last calibrated.?
Not necessarily a dealer-only job if you can find a local independent mechanic who has ET. In which part of PA are you located.? There may be an HEF member close by with the necessary equipment.
EDIT: Hooking ET up to the machine would also be a good opportunity to look at any Active or Logged Diagnostic Codes or Events. It may be that something in them might be related to the issue you have regarding implement control sensitivity.