Using a reflector on a go-to GEM mount

I have a reflector that I use on a Synta EQ6 Synscan GEM. The combo works pretty well, but there's one thing about it that bugs me. Apparently the optical axis of the scope is not parallel with the tube. When I do an alignment of the mount with 3 stars, the go-to works fine--but when I need to rotate the tube to put the eyepiece at a comfortable angle, the image in the eyepiece moves along with it. Then I have to hunt around to find the object again, and sometimes that is not so easy.

I was pretty careful when I built the scope to make sure that the primary and secondary were reasonably centered in the tube. Can the fact that I didn't offset the secondary away from the focuser make that much of a difference in where the optical axis is pointing?

Anybody else solved this problem before?

You are experiencing the non-orthagonality (sp?) problem of an optical axis not being parallel with a polar or even the tube axis. Very common. The offset of the diagonal has nothing to do with it.
The easiest way to correct is to shim the ota in the rings to make the ota/optical axis/polar axis parallel.
Polar align the scope but try to get the polar axis aligned on Polaris rather than the offset necessary for true alignment. With a moderate power ep, ota on "top", home position, shim the ota or rings to put Polaris in the center of the fov. Swing the mount in RA to the east and west side of the mount while observing the star. It should stay in the fov.
If you can, shim the rings at the mounting point to the rail, so that when you rotate the tube in the rings everything remains as close to parallel as possible.

Walt