"Just curious darrollr - how many hours does your 430?"
Mine is a 1988 430 and it only has about 920 hours on it. I'm the second owner. I bought it from my wife's grandad who is well over 300lbs. However he was a slow cautious driver so it wasn't really abused as far as mechanicals go, the body was just wore down. All the fender deck bushings and even the deluxe seat suspension internal bushings were completely gone. I have completely rebuilt the seat suspension, replaced all the fender deck bushings, removed and repainted every part from the machine, etc. that list goes on and on so better stop there.
"How well does it travel along the ground in forward and in reverse Does it jerk any when switching between forward and reverse?"
It was very jerky moving between forward and reverse. It was even jerky just moving the hydrostatic control lever to go faster or slower. However, nothing as bad as what you are describing. Although, I have read about others describing what yours is doing.
After breaking my spine in two places two years ago, I have just been able to operate the machine this season. I completely rebuilt the deluxe seat suspension and put a new high back seat on it so that the ride would be more comfortable. Major difference! Then I started researching to find out how to make it smoother and decided to check the hydrostatic dampener. It was still the original dampener from the factory and it was shot. I replaced it (AM133368 Torsion Dampener Shock/Gas Operated Cylinder $67.56). I also followed protocol for the Neutral Return Linkage Adjustment and checked all of the parts for wear. Everything looked good and I didn't have to replace anything there. The machine was much smoother after that but I was not satisfied and wanted it to be an even smoother ride. (I suffer from severe chronic back pain due to nerve damage and a bad spinal fusion).
"We got the (throttle/direction) linkage adjusted three years ago, but it started showing signs of getting back out of alignment after about 10 to 12 hours of use. We had the hydrostatic dampener changed out also, but I still could not see much of a change in its behavior."
I imagine that you probably have some worn out bushings or parts in your linkage that need to be replaced. It also may not have had the friction disk adjusted properly for the hydrostatic control lever.
I then decided to upgrade to the (Optional) Hydrostatic Transmission Damper Control Kit AM116222 (477266 - 999000).
This kit of course is no longer available from John Deere but they do still sell most of the parts individually. In short, I think this may be what you need to fix your problem. Even if not, it sure beats the price of a hydro pump/tranny. Here is a link to the correct forum thread where you will find a plethora of information about this problem and how to cure it. If this is not the fix to your problem then at least you will be in the correct thread to get information for your fix.
Even a Rev 4 Hydraulic Linkages Can Go Bad - Page 5
I sure hope that this helps you!