I'd like to suggest you go back to the beginning and follow through each step you've confirmed beginning with the battery. It is new and you've tested it off the tractor with a load tester, yes?
You've cleaned and tightened each part of the grounding cable and positive cable from the battery through to its final destination on the tractor, yes? All along each battery cable is secure with no cracks, burn marks, etc., yes?
You've chosen to remove and replace the ignition switch with a new one, yes?
You've changed the fuel filter and bled off the air, yes? You made sure when doing so that the shut off handle is where it's supposed to be, yes?
Regarding the glow plug circuit have you verified it is working properly?
When you turn on the key to the glow plug activation position does the light come on and then go off when the timer makes the switch open?
If the answer to the last question is no then you need to verify that the circuit is functioning as designed to. The relay is the big one on the firewall and it is referred to as a display unit by Kioti in their parts database. It makes the glow plug circuit function to help start in colder weather and consists of both a relay AND a timer to cut in or out as needed based on temperature of the engine, etc.
I just had mine replaced under warranty because the tractor would crank and crank and not start even in warm temps. I had to try to glow the tractor even though the light would not come on for the glow plugs, (when it had sat outside long enough to require assistance from the glow plug circuit). I know these are not your exact symptoms, but sometimes a circuit/relay may be faulty and render different symptoms for different reasons, for instance my timer may have flaked and your relay coil may have flaked...
Anyway, I would also suggest you post where your tractor is located, (state, town...) there may be people on the forum near you who could assist you in getting it running. Second pair of hands/eyes, etc.
And what about your dealer? Has he been of any help in assisting you to date? You might be able to get him to loan you some parts to try to assist in fixing the problem.
Anyway, one has to be methodical in their approach otherwise it is an exercise in futility jumping from one thing to the next.
Post back the remainder of your troubleshooting process to date so people can follow the logic and advise accordingly.