It appears that I've found a solution but it doesn't explain the problem. I'll get to that in a minute...
Hydraulic test results:
3pt shows between 800 and 1000 psi when lifting the 320 lbs of
ballast that I have loaded.
Chute rotation show 400-500 psi.
Blower lift shows about 800 psi. It's a short cylinder so things happen fast and it's hard to catch on the gauge.
When the noise occurs it shows about a 100 psi drop on the gauge. Again, it happens so fast that it's hard to get super accurate numbers.
All psi numbers appear normal per the manual.
Here's the kicker and what appears to be the solution. Since I've owned the tractor I've noticed that the hydraulic sounds while running in neutral always seem different when the clutch is let out and the transmissions internal pump is spinning. The 336D that I just sold was the same way. To date I've done all of the testing on the 186D with the clutch disengaged via the safety catch.
This morning I decided to let the clutch out during testing. I must have cycled the chute cylinder 50 times without any noise at all. Without shutting the tractor off I depressed the clutch and set the safety catch to keep it depressed. After about 10 cycles of the chute cylinder the noise was returning. Without shutting the engine down I once again let the clutch out and let the tractor run for about 30 seconds before I started cycling the cylinder again. No noise at all after 30 or so full travel passes.
I've studied the flow routing diagrams in the manual and I don't see how the transmission pump being engaged could effect the hydraulic pumps performance but it sure appears to. The only commonality I can find between the two is that they are both fed by the same factory strainer.
Richard