I have to choke up on the pick grip quite a bit and have almost nothing of it showing to properly play pinch harmonics. But there is so little of the pick left out that it's hard to play power chords or strum and other stuff when I'm holding it properly for pinch harmonics.

Do people typically switch their grip on the pick back and forth in the middle of songs, or do I need to modify my technique for pinch harmonics to where enough of the pick is sticking out that other techniques can be used without changing grip?
in my opinion re-learn to hold the pick with more of it exposed
Epiphone Les Paul Custom
Ibanez RG550

Vox AD30VT
I remember having to do the same thing when I first learned pinch harmonics. Once I got the hang of it I didn't have to change how I held the pick. If pinch harmonics are the only time you're changing how you're holding the pick, then try doing them without changing it. You just have to angle your hand/wrist a little bit different when doing them I think, its hard to say exactly what I do now because its been so long and I don't even have to think about it.
You should naturally develop a way to do it without thinking, just as you naturally develop muting technique