I was 9 cm and +2 when I arrived, and pretty anti-intervention.
These are the things I would look into...
I was only allowed to birth in the pool if I had completely clear amniotic fluid. So they had to break my waters to check that. I was ready to deliver pretty much on arrival, but if I had spent first stage in the pool, maybe I would have had to get out to have a cervical check and have my waters broken?
My husband took the baby to the warmer and rubbed her vernix in while they got me out of the tub and into the bed. That was fine with me - I wouldn't have wanted to carry her, but maybe others would prefer something else?
I had in my birth plan - no bath, Vit K if bruising, no Hep B, delayed eye drops, complete rooming in, no artificial nipples. We decided against the eye drops, and nothing was said. No-one commented once on the Hep B, I was strongly advised to have the Vit K, which we had in the end, due to bruising, but I wish I had bought drops.
They did the hearing test in our room, as well as the newborn exam, which was done by a nurse practitioner. She put her finger in the baby's mouth to pacify her, else she would have had to come back later when baby was sleeping. Emmeline was 8 lb 2.8 oz, at 39 weeks 5 days, which was considered big for dates. (Cut off for 39 weeks is 8 lb 2.5 oz I was told, and she was closer to 40 weeks anyway). The L & D nurse said apologetically that she was supposed to do heel pricks for blood sugar every two hours, but I could refuse, so I did. We checked at 24 hours instead, at the same time as the PKU, and she was fine.
We pushed for "early" discharge, which is 24 hours after vaginal birth, rather than the normal 48 hours. She was born at 4 am, we left at midday the following day.
Hope that helps, and good luck with your decision!