I know what you mean about Muro tears. My horse has a number of eye problems (uveitis and secondary glaucoma) and we use hypertonic saline ointment in his eye when he's having a uveitis flare up. I feel so badly, as I know it burns.
Maybe give a night time ointment a try---I don't think it could do anything to hurt (though maybe ask your opthalmologist first). I would think if you needed the Muro drops, put those in first...then put the ointment in before bed. For me personally, putting drops in and then coating the outside of my eye with Aquaphor would not do the same thing.
Also, maybe talk to your doctor again. You mentioned that the Muro tears moisten your eye for a little while...which makes me think that your eyes are dry, and you want moisture? (makes sense, the whole 'not closing completely when you sleep and getting dried out issue'). Again, what I know about hypertonic saline is only from treating my horse...but my understanding of hypertonic saline is that is draws moisture out of the eye, reducing inflammation (I think in the packaging, it talks about treating 'corneal edema'). I don't think your doctor has you using hypertonic saline as a moisturizer, but I could be totally wrong on this. You just might want to discuss it again with your doctor---why she has you using hypertonic saline and whether there's another product that you might also use if what you're really after is relief from dryness.
Hope that helps,