I believe I figured out how to simulate something more like the reality of linear bearings in my design. For anyone interested, I used contact elements in ANSYS. I setup my model so that there was a gap between my linear bearing and the rail and then setup contact pairs between the bearing surfaces and the rail using separation only always and selected key options to close the gap before starting the analysis. A refinement of this which I might look into would be specifying the compliance of the coupling. I could use this to simulate the compliance of the THK bearings from catalog data.
Attached is a screen shot of the displacement of my test model. It's a vertical rail constrained in x,y,z at the bottom of the rail. It has a bearing on it, and there's a vertical piece that holds the bearing from the top of the rail (sort of like the screw in my real design). There's a big block attached to the bearing with a cylinder (cutting tool) coming out the bottom, similar to my milling head. There's gravity applied as well as a force in the y direction on the cylinder. You can see the bearing has slid down the rail and that the block has gone down with it and twisted to the side. Harder to see is that the top of the rail has deflected in the y direction in the opposite way. The bearing is transferring the moment applied by the force on the cylinder into the rail and deflecting it in the correct direction.
So now that I know how to model this I can go back to working on my frame design.