It sounds like an acoustic guitar piezo pick up through an amp that's miked to me... that is, overly bright and brittle, but also that's just the sort of sound they tend to make. You can try rolling off some of the highs if you like - it really can't be sounding much different in the room.
I actually do something similar sometimes but wouldn't use it as a main sound.
It sounds worse when the lead cuts in, that's for sure.
I'd record the guitar on its own, sans pic up and amp, with the 57 (assuming that's your only mic) then re-record through the amp with the highs rolled off and put them together, probably 75/25 to just the guitar and see what that sounds like. You'll lose some highs with the 57 on the guitar alone, probably, but that overly sheeny recorded sound via the amp can help bolster it a bit.
Obviously you have to have good "repeatability" with your playing to do this or it will get very messy...