A.,
When my third child was born we too were cash pay. My husband was self-employed at the time and like you we had private health insurance but it did not cover maternity. I did have to have a c-section due to the fact I'd had one previously. If your ob delivers at more than one hospital definitely go with the hospital that cost the least. My ob only delivered at one hospital so I was limited on choices. Make sure everyone you work with (doctors, hospital, lab, ect.) know you are cash pay and ask them if they offer a cash discount. Also, they may offer a larger discount if you pay all at once vs. installments. But remember most of them will want to be paid-in-full before the baby is born (the hospital and ob).
Also, make sure you read over your insurance coverage beforehand. In my case even though the baby was covered from the first breath my plan specifically stated it did not cover any charges associated with newborn care following a normal delivery. Which ment it did not cover the pediatrician's visits to the hospital, or the hearing test, or anything else done for the baby while we were in the hospital.
One last thing, although it was not an option for me, remember a birthing center will probably be cheaper than a hospital. I don't know if you are open to that but it is something to think about.
Good luck and I hope everything goes well for both you and the baby.
A.