Good news :) They are going to accept the $2093 from our insurance as the complete payment and will hold the $2000 from our HRA and apply to the bills from the delivery in April. Thank God.
Unless they go back and tell our insurance they accepted a partial payment (which I don't think they will bother doing) this actually means we hit our deductible, saving us $1000. The woman I spoke too was very very nice and helpful. She said to call her after I have the baby to reduce those bills too.