DS1 was born at 1 am ... had to hang around in hospital all next day waiting for doctors to discharge me. Didn't get released til about 4 pm. (So 15 hrs).
I wanted a 6 hr discharge from hospital, direct from the labour suite, but ds2 was born during the night (c.11 pm), and they said it wasn't possible, and I had to go up to the ward, but woudl be able to leave at 9 am. Come 9 am I had to really fight to be allowed out, they were extremely reluctant for me to leave without being signed off by paeds and obs. Eventually they agreed if we stopped off at the GP's on the way for the GP to check the baby! (What utter rubbish - the midwives in the hospital were a lot more used to seeing a newborn baby and checking it was OK than the GP who rarely gets to see a baby that young Anyway it was a treat for clinic and GP to see him, especially as I had been in there 18 hrs previously moaning about how fed up I was that I was overdue and nothing was happening!)
I completely understand your pov re hospitals - I loathe them, and just wanted to leave as soon as possible.
So my advice would be check the hospital's policy on 6 hr discharges direct from labour ward, and if they are allowed even for first time deliveries, then try and be assertive (or get dp to be assertive for you), and decline to leave the delivery suite and go up to the ward if it isn't necessary.
Of course there are many and varied medical reasons why they might want you to stay in a bit longer for monitoring, and I wouldn't counsel ignoring that advice. But if you're both healthy and fine and it's not against their policies, then you may still need to be determined to get what you want.
HTH