OK, it the fly sparging changes my diagnosis. I will again make an assumption that you are using a braid or manifold in the MT and not a false bottom. Either of those are more susceptible to channeling and that could be the problem or part of it. Wort left behind after fly sparging should have very little sugar content, so that should not be an issue.
How well did you stir the grain bed and did you stir it near the end prior to beginning the sparge? That can improve the lautering efficiency considerably and it goes a long way to help prevent channeling problems.
There are varying opinions on fly sparging technique, but I've had the best results by not draining the grain bed completely. I maintain an inch or two of sparge water above the top of the grain bed all the way to the end. IME, this helps keep the grain suspended in the mash for more efficient lautering. This method has worked very well for me.
I doubt that it's a problem with your hydrometer, but it could be. They normally don't get "stuck". I've never seen that happen. It's possible that the internal paper scale has slipped, but if it reads zero with plain water it should be OK. I suppose that you could get one that was not manufactured properly and that could result in a non-linear error that might be more difficult to detect. You could make up a sugar solution of 1.040 SG to check it in the range that you will be using it most of the time. That will tell you a lot. Yes, buy or borrow another hydrometer to eliminate that question.
I really think it is a channeling problem and maybe a problem with the crush as well. It's got to be something major to affect the OG that much.