We found that the moby wrap and the beco butterfly were the best carriers with our preemies when they were 5-10 pounds. Both Zephan and Micah preferred being carried upright (helps with reflux!) and it seemed like both of these carriers were comfortable for this. As far as breathing, make sure the baby's head is well supported. If you keep the baby in a "frog" position, much like what you would do for kangaroo care, with their chin slightly up, the baby should have no trouble breathing. If you have taken infant CPR, remember what you do to open the airway? Tip the baby's head back slightly. Same idea. When we did use a sling, we would fold a swaddling blanket and put it behind the baby's back to make the space in the sling smaller and more supportive.
And obviously, with the baby in a carrier, you can feel them breathe!