Cindy, your assessment of this case as being reflux sounds like a good  one.
With such a large weight gain in the first month and the description  of
coughing and gagging at the breast, these are the typical signs of  hyperlactation
and overactive let down.
Has the mother tried the side lying position?  I find this works well  with
these babies.  The milk can pool in the cheek and allows the baby to  form a
bolus to swallow.  I find the football hold the most problematic,  with the milk
shooting to the back of the throat and the babies not having any  time to
compensate.
In the Lactation Consultants Series there is a chapter on over active let
down and over production.  It may be helpful.
I find with reflux that small frequent feeds are best and tummy time after
feedings helpful.
Ann Perry, RN IBCLC
Boston, MA

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