That's all a beam splitter is, a half silvered mirror. Take a look at the Edmund's Scientific stuff.
That's why I think building to tolerance is a tough plan. You have to build with the plan to shim as required, and do it empirically.
I'm sure someone here knows how, but truth be told I'm certain I cannot calculate how the wavefront of the image changes with some parts going through one sheet of glass, and other parts going through two sheets. I know that affects the physical distance because of the transmission medium differences in the paths. But not in any way that I can predict.
So, you build adjustment into the device, and you tweak!

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