My experience. Some years ago, I played in a band, using a piezo-equipped guitar (it also had coil splits). Seems like every time we came off the stage the other guitarist complained that he could not get the crisp clean sound I did. (That is, when I did not have drive engaged for overdrive). FWIW, I was using primarily a Mesa multi-channel, with one channel set for a "Fender-ish" type clean, meaning scooping the mids a bit. I had to remind him that he was playing a Les Paul through a Marshall half stack, all set up for big THICK sounds. He never quite seemed to sort that out.
I would try rolling back gain and mids and experiment with the master, if applicable, to avoid overdriving that channel, to see if you can get where you want to go with your current amps. If not, try to test drive some sort of classic Fender style.
Also, since you have an acoustic amp, you will almost certainly get a nicer blend if you separate the outputs and run the piezo to it.
FWIW, the last gig I actually did, I used a similarly set up guitar with the magnetic and piezo going into separate channels of the same amp.....solid state Quilter Aviator combo if you can believe that. With an ABY pedal, was able to blend the two on the fly and the results were great.