This may be quite a bit of your issue there....I used that same little speaker once or twice, experimenting with all the different types of things I could connect to the axe, didn't like the results.
Also, tweaking on cans is going to cause.....issues.....
I remember a mix I had done, only on cans, excitedly played it back on a sound system at the band room, and I have never been more embarrassed!
I'd recommend something like some reference monitors or even a small (quality) PA to tweak like the zxa1, you will get WAAAY better results, I guarantee it.