Although this is an old thread, I'll post a solution I just found that fixed the "flakey shifting" problem on my 2011 DK35SE HST.
Over the last couple of months I had an increasingly difficult time shifting from Medium to High range. I tried lubricating everything as noted in this, and other threads. Today I could not shift to High at all. The shift lever would hit the front stop on the tractor frame before it had moved the gear far enough to engage in High.
Taking a closer look I noticed the spring pin that attaches the shift arm to the shaft that goes into the transmission was protruding to the rear. I used a hardwood board and hammer to push the pin back in, and that fixed it. I am fortunate to have found it before the pin completely worked its way out.
A pin was also protruding a bit toward the front of the assembly, and I thought it might be broken. However, it appears to be a spring pin inside another spring pin shown as parts 2 and 5 in this diagram from Michigan Iron:
Parts Finder Michigan Iron & Equipment Morrice, MI (855) 265-459
The inside pin was wobbling around inside the outer pin. It may also explain an intermittent I starting problem where the range selector showed being in Neutral but the starter would not engage. Perhaps it caused the range potentiometer in the control circuitry to send out a flakey Neutral-range signal (there are two values), thus preventing starting.
Anyhow, if range shifting is flakey another possibility might be the spring pins on the shift lever shaft.
ADDITION TO POST: In reading my post the forum's suggestions led me to this other post where K0UA had the same suggestion:
https://www.tractorbynet.com/forums/kioti-owning-operating/319454-dk40-high-range-not-working-post3863176.html#post3863176