Cursor location in World Space, LookAt rotation and Gimble lock.

No further advice unless I actually go and do it I’m afraid.
I think the issue is how you are getting the cursor position.

Why not simplify it and just add +1 if the mouse is the the left, -1 if to the right. etc. ?
You could even end up driving this by the distance of the cursor on the screen - so the further it is, the faster the turn rate
to do that
cursor location x / screen size x = - the screen position in 0 to 1 range.
From the 0 to 1 range just set up a set of >= .25, .5, .75 - and instead of just a +1 you +1, +5, +15…

if done correctly it should work fine on both axis - and the object axis you want to affect are probably Z for left to right, and X for up and down.