Karl Townsend wrote:

...
Since most of us don't have farms / orchards or use these items, a link
to them might help us understand the issue.

Sorry, I couldn't find a good link. An airblast spray has a huge squirrel
cage fan hooked by a gear box and belts to the tractor PTO. the air from the
fan is nozzled down so the air leaves at over 200 mph. Takes a lot of
horsepower to do this.

So this is basically a leaf blower on steroids? Unless something is
loose in the drive line, this should provide a very stable drive line
loading.



The "bucking forward to reverse" description makes it sound like
something is momentarily freeing up and jumping forward only to have the
drive slam into it a fraction of a second later, i.e. uneven loading on
the drive.

Adding rotating mass somewhere in the drive should change the resonant
frequency. Also, you say slowing it down a bit helps, can you speed it
up slightly to change the frequency without hurting performance? bumping
up to 600 PTO RPM isn't likely to critically over speed anything, but
might get you out of the resonant range.

The harmonic dampers on an engine are basically a balanced flywheel
mounted to the rotating shaft via an elastic (rubber) coupling.

I'll try the rotating mass idea by just boltinh a plate to a large pulley.
Thanks, I wasn't thinking this simple. Still, if there was some way to have
mass with the elastic coupling, it would work far better. i just have no
clue how to build this.

I don't know what your "bolt to large pulley" setup looks like, but if
you can have oversized holes in that plate and fit rubber tubing around
the bolts that go through it you'll get your elasticity. use a rubber
washer on each side of the plate as well and some secure stop like
nylock nuts, double nuts with a lock washer between, castle nuts and
cotters, etc. so the bolt connections are secure without being over
tight.