True Freezer door swing change - True 35 cu. ft. / 991 liter Commercial Freezer T-35F

SOURCE: freezer is short cycling ,thermostat

To me it sounds like, from what I am reading that your compressor may be the root cause if it is short cycling and you changed the thermostat and moved the thermocouple and the problem persists. Was this working fine till recently or did you just aquire the freezer and noticed it is not performing correctly?
Here's the simple procedure I use whenever I run into one that's 'short-cycling' (trying to start, clicking on/off every few seconds, or in some cases, every minute or two).

Basically, using a digital ohmmeter, you pull the compressor's relay and overload off its three terminals, then check the resistance between each of these three pins. Older relays looked a bit different than the solid state ones, but pull off pretty much the same way.

First note the two pins that read the highest resistance. The one that remains is the 'common', to which one end of both the start and main windings connect. (The common's not always the top pin, so you'll want to do this test to be sure)
Reading from that common to each of the other two, carefully note each reading. Then measure back across the two with the highest resistance, ignoring the common. That reading should be the exact total of the two individual coil readings, because you're reading through both coils in series now.

If those two sets of readings aren't within about 1/2 ohm of each other, then one of the compressor windings is shorted, and if it runs at all, it'll run hot and usually end up short-cycling on its overload protector. If the windings test OK, but it still won't run, then I connect a test cord and try to run it manually. If I can't start it that way, it's most likely a mechanical problem, most often binding bearings, and the 'bottom line's the same: either the compressor or freezer will have to be replaced.

Did the new thermostat come with an adjustment screw in the back? if so you might want to play with that as that can also cause this issue if it is not set correctly.