I've had considerable success in placing the camera lens, usually with a lens hood attached, directly against the protective glass and holding the camera firmly in place. Lengthy exposures pose no problem and so flash is not needed. This takes care of both reflections and camera shake at the same time. It may necessitate a lens change to a shorter or longer focal length, depending on the subject.
I've found that if I explain what I'd like to do to the guards, they don't have a problem with it at all. I've some lovely prints taken in the Anchorage Museum using this technique.