The jerking is your lock up on the torque converter locking up and releasing. The internal slippage through the torque converter must be below a certain percentage and the TCU will lock up the torque converter for cooler operation. I'm not sure why engineering didn't install a metering check valve in the lock up circuit to slow the rush of oil slightly so the clutch didn't bang so hard. The product improvement program for these transmissions stopped many years ago.
CTM84 or the newer version is your manual. I'll have to look tomorrow for the parts manual number. Unfortunately Deere lumped all their DF150, and DF250 transmissions in the same parts book. I requested the Bill of Materials for my transmissions in a DTAC case at Superior Diesel to get all the part numbers that built mine.
Most parts are available from a John Deere ag dealer. You will have to use a John Deere Forestry dealer for the gaskets, torque converter lock up plates, and a few bearings(Ag dealers aren't allowed to sell these). They are not bad to rebuild, but I have an eye for details and experience with other powershift transmissions. Careful, if you need TC lock up plates. The originals are NLA. There is a way around this and will save you $1500. If you get into yours, I can give you a list of heavier bearings and a supplier I use from California. I use straight roller and spherical roller bearing in most positions. Mostly SKF bearings. I run Schaeffers 204SAT All Trans Supreme oil in the transmissions. This oil is pricey, but handles the high heat very well. It's too time consuming to open up a transmission prematurely due to an oil caused failure. Keep your radiators clean!
Transmissions can be calibrated for better clutch pack engagement. They will never be as smooth a a Cat transmission. Friend of mine calls them funk-sional.
You said you had to run a gallon overfull to make it work. Are you checking your level with the engines running, bowl up for the front trans, bowl down for the rear? I only run mine at the add mark, as the oil expands so much when it gets hot.
Check the play in your torsion dampers at the rear of each engine. With the engine off, turn your transmission input drive shaft back and forth. If you have more than 3/8" travel, your damper is wore out. If you let it continue, eventually you will break your drive shaft. I have access to new dampers from the same manufacturer that supplies Terex. Less money.
Check and change your hydraulic pump drive oil frequently. The housings are no longer available. Salvage only.
Install a brass plug in the bottom opening of your engine bell housings with a tiny hole in the center to let any oil out. Run a wire up in the hole once in awhile if they show damp to clean them out. This will prevent any dirt from getting drawn in and packing in your starter drive.