Well, the cheapest cans and software are not the same thing as good phones, it just doesn't work that way. The Sonarworks works best with the good phones, flattening out the last weird whistles, but trying to wrangle bad phones into submission is an exercise in futility. I've used Sonarworks with all my cans: Beyerdynamic 770, Sennheiser HD25 and 600, AKG240, AKG 271, AKG550. There's really no comparison and they sound nothing like each other even after the Sonarworks correction. Sennheiser HD600 isn't prohibitively expensive, but it is a world standard in studios around the world that will last you for decades. My own pair just turned 19 and still going strong! One of the best purchases and perhaps the most used piece of equipment!
You should find a pair for $150 used if you search for a while.