Have you tried a trackball? They are much more precise.
I use a Marble Mouse from Logitech. It is a trackball, but they
probably feel they have to call it a mouse.

I use one in work - they're great for "normal" work, but a bit crap
for gaming IMO - the ball on the marble mouse is too big, whereas the
first one I had by Logitech (forget the name) was great - small
central ball and two HUGE buttons either side.

It hardly ever needs cleaning. ;-)

I do mine every couple of weeks, and for the benefit of the op, while
this might sound onerous, it's literally a sub-10 second job - the
ball lifts out (no need to disassemble anything, it simply lifts out),
and you simply knock any big lumps of "snot" off the three ball-
bearing mounts.