My shuttle shift DK35SE starts and runs fine, hydraulics all work too. Hours are almost 300.
It was started up fresh one morning having run OK until it was started that day. At first it crawled very slowly forward-maybe 1/2 mph, very creepy when placed in forward after a bit of warm up.
I wondered what was up so tried reverse which seemed OK so then I went back into forward and it was acting normal again.
I drove it maybe a quarter mile to a tree I'd dropped which involved driving up a steep slope then backing down (call that trying to back down) a skid trail to the tree. As I corrected my tractors position on that trail I noticed it had lost powered movement and proceeded to allow it to roll downhill to the base of that tree I'd dropped.
After some crawling around underneath I decided I had no idea what was up. That was in April and given that my own shops entryway is blocked with two large piles of lumber on sticks drying under an open roof, I had it hauled to a nearby repair shop then another, after the 1st place stopped work due to issues between the buildings owner and his son.
2nd shop due to lack of parts on other tractors already broken down has left it waiting since late May.
I saw no issues with the shuttle linkage when it was dead in the woods. My thinking is toward a broken gear or shaft?-> the clutch seems normal.
The OP's issues resemble my own Kioti.