Bedding/shimming/thermofit does not eliminate the shift.
I got 2nd place overall in Gas Gun PRS this year, and in talking with the guy that got 1st place (also a couple of the other guys in the finale gas gun squad) we see the same thing. 0.2-0.4 mils of elevation change in POI going from a bag to a bipod. We were mostly all using Aero enhanced (beefy barrel mount area), JP, or Seekins uppers, or something of that style. It was dead repeatable every time.
If you lock pretty much any AR-15 FF handguard into something like a tank trap-- like lock it down hard so it's wood-aluminum-wood with tension, it will shotgun pattern. If you torque the bipod left or right it will string shots left and right.
Here's the thing, the upper rail holds your optic, the upper receiver bore holds your barrel. ANY movement of the rail or the receiver bore is pretty much directly causing POI error. The barrel extension has something like .845" of "wheel base" in the upper. 0.2 mils over .845" is 0.000169". So whatever loading you do on the handguard needs to cause 1.7 TENTHS of deflection to the mouth of the upper. Not surprising that it happens.
We get spoiled with separated chassis/receiver setups in bolt actions with steel receivers-- Larger diameter (more rigid) larger clamping forces (more rigid, less slop), and steel on steel (more rigid), plus the chassis/stock and receiver are separated from each other. AR's are a different world.