Google’s photo scan app deals with this by taking multiple overlapping photos at each corner, then using math to get rid of the glare areas.
You might be able to accomplish this manually by taking different photos while rotating the photo so that the glare ‘moves’ to a different part of the image. Then, when you are doing your stitching in Photoshop, add in the different versions, align them, then reveal only the ‘good parts’. I did something like this with a series of photos my wife took of a family photo that was in a domed glass frame that couldn’t be removed. It took more work than it should have, but I did get a final photo without glare, reflections, and whatnot.
Perhaps not helpful, but a possibility.