I also keep a low bar position while doing good mornings. But I've never had a problem with the bar. My bar position is very tight, my whole upper back is tight, the bar has no space to move. Also the arms and shoulders help to keep it locked in. All this with a neutral spine and neck.
This is about the straight leg variation to work the hamstrings.
This I must give my 2 cents. I think that the hip hinge should include a natural knee bend (only a little) while sitting back/leaning forward. This holds true in the GM, but also in the RDL or similar hinge exercises. Knee's shouldn't be locked straigth in my opinion. I've never understood why this would work the hamstrings more anyway. It maybe stretches them more, but then again stretched muscle produces less force.