Kinda been where you are...this is my experience...am Scottish heritage myself.
I've learned...low end Craftsman wrench destroyed itself too soon. Trying to break loose a nut takes both high torque and lots of air.
Thus, I bought a HFT impact wrench...highest torque they had...I hefted several, one was toooo heavy so I went one step down as regards weight. I think it's a half inch.
I added some old propane tanks for extra CAPACITY...just ran hoses and shutoff valves from one to the next and to my compressor. Before I did this, I ran out of air fast and compressor ran all the time at too low PSI.
Now, I use a wrench to break loose the lug nuts, then the impact to spin them off quickly. Impact spins them on after I start them by hand but ALWAYS do final tightening by hand...else I end up with wobbly rims after a few minutes...don't ask how I know...
I find impact to be really, really handy, but not a complete replacement for the 4 way such as you, and I, have.
I truly believe that your small compressor does not have sufficient CFM air to get the job done by itself. However, if you can find an additional tank of some size and add it, then you will be amazed at how much difference it makes. Do this and get a 80 dollar HFT impact wrench. The high torque results in using less total air than a less powerful impact wrench...thus you actually get the job done faster with the same compressor/air capacity tank.
good luck...and keep your wrenches handy to break loose the TOUGH nuts.