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no problems
You can still use drift alignment.
Point to a star on the meridian and make the correction then point to the lowest star you can see at 40 degrees. You don't usually use stars right on the horizon anyway. At 40 degrees you'll get a component of the error in both altitude and azimuth. The overhead correction will correct most of the altitude component first leaving the azimuth component at 40 degrees.
It's not perfect and it is an iterative process. You will need multiple cycles of the two.
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