I normally view with my glasses off. Mainly it is more convenient. I am only slightly myopic. I have never noticed the effect you mention but it sounds like some possible internal reflection in the glasses. As you say you are profoundly myopic I would suspect that your glasses are quite thick, particularly at the edges.
Usually you will require a small change in focus to compensate for correction caused by the glasses. When I am at astronomy nights I always focus with the glasses on. That way the scope does not need refocusing for the average viewer.
Barry
PS Some expert say that myopia is a sign of superior intelligence,