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Jim, I used a Lee square linear polarizer, before I returned it. (Nothing wrong with the PL; I was experimenting with cross-polarization for variable neutral density. Didn't work out). The quality of the filter was, as expected fine, and I didn't see any color issues when it was used alone. If you want to use only a conventional filter holder but don't want to rotate it, then you can, as you suggest, insert it at 90 degrees. That may or may not result in a choice between maximum or minimum polarization; it depends on what the optimum angle would be for the particular items in the scene. If you are only concerned with darkening the sky, then I think (but not sure; maybe someone can verify) that the polarization axis of the filter may be designed to maximize polarization with the filter upright (square to the horizon). But for reduction in reflections etc. on other objects, the optimum angle may not be square.
Lee does make a supplemental filter holder for the polarizer that mounts on the front of the normal holder, and allows for independent rotation. I don't have any experience with it, but that would allows you to both use a grad in a fixed position, and rotate the the PL for the desired effect.
Or you could use a threaded polarizer on the front of the lens, and mount the filter holder to that. That's what I do, and I'll admit it can be a little fiddly to attach the holder to the polarizer and then rotate each separately for the desired effect. But it allows me to use a B+W polarizer that I'm very happy with, and which I use alone (without any square filter) the majority of the time.