I guess it depends on what brand of rings you choose. Each manufacturer has different heights and even which base you get can add to the mix. I went with Warne Maxima bases and rings because of their reputation for being extremely strong. And yes, they're heavy too, but I have all the faith in the world that I bought the best rings.
I went with medium height rings with my .223 24" barrel with a Bushnell Elite 4200 4-16X40mm. I believe that I may have been able to get closer to the barrel, but not too close, with the low rings. But, I went with the medium rings so that I would have "thumb room" to cock the hammer. With low rings you may have trouble. That was something you didn't mention in your post - need to consider it.
Ranger413