Kohler CH20S hesitation

This engine which was retrofitted to a JD318 about 18 years ago and rebuilt last winter now performs great except for random hesitations where it sorta dies down to about 1/2-3/4 rpm like it's lost its pace. When it does this, it can only be corrected if it's throttled all the way down and then returned to full throttle again--just a 3-second maneuver. It's a somewhat similar sound and performance to pulling out the choke but is more precise with a steady but attenuated speed and no choking sounds or fumes. The most accurate comparison is what I get from my Model T when I retard the timing lever, but probably most of you aren't familiar with that!
Here's what I've done and gleaned so far:
   Gas tank was cleaned and dry with new filters on the intake hoses
   New fuel filter
   Examined and manipulated governor when it's doing this and everything seems free and normal
   Very random with no patterns as far as slopes, roughness, mowing load, etc.
   Can't be recreated by choking, nor will manipulating the choke correct it--only that throttle maneuver
I'm lost and hope somebody has some suggestions. It's really not much of an inconvenience to flick the throttle, but it just isn't running perfect!