To fix your issues with needing to move the stick too far to register inputs…
Open up the stick and remove the gate to reveal the actuator, and wrap even layers of tape around the actuator, trying to make it look as neat and even as possible. By enlarging the actuator, you reduce the distance you need to push the stick until it registers an input.
Add a little at a time, you do not want to add too much and then discover you’ve made the deadzone too small. A deadzone that is too small will result in more unintentional inputs from when you release the stick or it go to neutral.
As for the looseness, you can replace the spring with one from another stick that is stiffer… though imo at that point you might as well just buy a Sanwa JLF to replace the stock Hori stick and be done with it.