I left the rings on. It looks odd, but emergencies happen and someday I might be awfully glad I left those rings on.
If they are tight enough against the noseband (like 3 of my Micklems) I just flip the ring as far as it will go and they stay up (and it looks really odd.) On the other Micklem I had to use string to keep those rings up. The lesson horses I ride seem to prefer it this way. This way I can use a doubled up flash strap with keepers to serve to keep the horse’s mouth shut, but I have yet to ride a horse this past decade that really needed this (what they needed were light, sensitive hands and well timed hand aids.)
Without the flash strap you will be able to lower the bit in the horse’s mouth. Try and find some of the Micklem Warm-blood length bit straps, that way you will be able to get the bridle so it looks better on your horse between adjusting the bit straps and the cheekpieces.
The noseband itself ends up sort of floating above the nasal bone. Again it looks really odd but in over a decade I have yet to have a horse indicate to me that the floating nose band irritates them or interferes with their vision at all.
I just want to kiss your horse’s nose. Do anything you can to make life more pleasant!