Edit to respond to your edit: That's a great idea, lowering the action to lower right hand force. For me the force in both hands is very much linked, so if I can back off on one it ought to help the other.
This is very normal, a mental quirk for all of us.
If we can't hear ourselves, we tend to pluck and squeeze harder. It just happens.
The comments above about turning up the amp and letting it do the work are spot on. In your general case, the bass should feel too loud for you, so you'll have the instinct to pluck (and fret) lightly and softly so the volume is right. This equals less stress on your hands.
New setup for low action is also appropriate for you. Take it to a setup tech for a better job if you don't feel up to it.