That is where we had it happened the most. Listen to the little "thing" between chorus and verse in Ed Sheerans "Perfect" as an example. Goes from Ab - Eb/G to Fm. We can't make it sound like that.
He is not using a lot of distortion BTW.
Compositionally, that would seem to work fine.
Is it possible to play the inversion in isolation from the rest of the song?
You might try detuning the 3rd in the bass (tune it to the guitar chord) just to see if it's the dissonance due to equal temperment.
If your tone is bright with strong overtones, moving your tone towards more fundamental should help also if it's just a dissonance problem.
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