The ignitor, as Eddy as stated, is rated at 300 watts. Plus the fan and auger supposedly have a rating of 25 watts. At best we are talking 3 amps max. However that rated consumption is after the element has stablized at its rated power. At start up the current can be 2, 3, 4, times, or more, the rating due to the type of material the element is made of. By using an ohm meter find the cold resistance of the element then divide the voltage by that resistance. That will give you the cold start up current in amps.
Also the wave form of the inverter, power supplies and other electricial devices may have a sensitivity to something other than a sinusoidal (sine) wave. The Colemen may not comply to its needs. You may have to ask about that from the design engineer of that digital board. Treager may know the answer or surely should be able to find out. Or try a known better power supply.
There is a reason why you can buy a 2500 watt inverter for $400 and another rated the same for $2500! You may have just found out why.
Peter