Hey again TGG,
Thank you so much for the advice (and validation that this is heckin confusing haha). After a lot of fiddling, I was finally able to figure out the string of issues that was causing problems. In case anyone else ends up finding this later in search of help, here's what I ended up doing to solve my issues.
Firstly, as it turns out you can't just use the yaw of the head, since that doesn't account for the model rotation. The headNetYaw variable calculates that difference out, so unless you mirror that rotation, you're better off using the variable itself. So I switched back to that method.
To get around the issue of having multiple poses, some with fixed head position and some with dynamic, I built in some methods to the model class to check the entity's pose and return the proper value for the head position. I designed them to return either the raw version of the variable (needed for the item rotation), or the calculated one (needed for the rotation of the actual model parts), which allowed me to ensure that the proper result would be returned in both cases. This avoids the issue of having to write up a checker code within the item renderer itself, and that way I only have to worry about changing one set of code if I make any tweaks.
Lastly, I finally figured out the biggest stumper, which was the fact that the rotation was still crooked even with the synchronized method. I tested each one individually by forcibly returning zero on the two I wasn't using, and determined that individually, they were all doing what they should be. However, they were messing up when combined. As it turned out, I had the order of rotation different on the item renderer (pitch > yaw > tilt) than on the entity model (tilt > yaw > pitch). Changing the rotations on the item class to match the order of the ones on the entity model solved the problem. So it did indeed come down to the order of transformation in the end.
Definitely one of the tripper problems I've dealt with, but I'm happy to report I finally have it solved. Thank you guys again for your help!