I think the cycling thermostat's internal heater should have continuity.
Should read between 5600 and 8400 ohms.

Lets say it measures 6000 ohms. On a low heat setting (selector switch is at 10 ohms) so you have 6010 ohms total, this internal heater runs at its highest setting switching the thermostat contacts on/off often so low heat. On a high heat setting (selector switch is at 10000 ohms) so you have 16000 ohms total, this internal heater runs at it's lowest setting switching the thermostat contacts on/off less often so you have high heat.

The thermostat contacts are
switched by the heat from the main element plus the heat added by the above internal heater.

Earlier you said you shorted out two wires on this thermostat if the two wires you shorted were the internal heater you may have blown the temperature selector depending where it was set. If it was at the lowest heat setting (10 ohms) you would have put 12 amps through it, I believe that amount of current would blow it but am not sure about this.

Normally the operating thermostat should open at 155F and close at 130F, if this is with no internal heater at all it gets heat only from the main heating element. The cycling of the thermostat changes when you add the heat from the internal heater to the equation. With the internal heater blown the thermostat should still cycle.

Here is the link to the parts
Model LER4434AQ0

You need a Hi limit cutoff (fuse) with an open contact temp around 350F looks like the kit you bought is 309F.

Normal if the operating thermostat contacts weld together the unit will run on the high limit thermostat. Symptom is you only have high heat. If it welds together the thermal fuse blows as a safety device. That is why they sell the Hi limit and thermal cutoff (fuse) together. I would replace them all.

Here is the wiring diagram, print it, easier to trace out the circuit than having to refer to the back panel all the time.
https://www.servicematters.com/d...0Sheet%20-%203396197.pdf

Yes you can run it with the back off.
Check to make sure you have good exhaust flow. May want to check/clean your blower wheel, they can get clogged/coated with lint which drastically reduces air flow.

Hope the above makes sense!!!