If you are burning too hot you need to turn the power down.
I suggest you try welding some thicker material to get practice with. Using gasless mig wire in 0.030 or 0.8mm should handle the 0.125" about 3mm really well.
Something is not right here. How many amps is the machine rated at?
Here are some photos of some welds done with a gasless mig welder here:
Gasless mig welder
The thickness of the metal welded in those photos are pretty close the the thickness you are welding. I think those orange beams would have been about 2mm thick.