mOxxie, if you can talk to the charge nurse on the L&D floors while you're touring, *her* reaction (and advice) when you tell her you'd like to delay cord clamping should give you a good feel for how supportive the nursing staff would be (which in many cases could be helpful if the random doctor who's caring for you is not so supportive).
When I knew I wanted delayed cord clamping and AAP procedures followed for dd2 for breastfeeding initiation (I didn't know as much about them with dd1, and assumed that's how hospitals did it, and when they didn't, with Ina, I figured that they must have had a reason. The reason was that I hadn't told them I wanted that, therefore they did what was most convenient for them, which was whisk baby away to do their thing with her immediately rather than letting me initiate breastfeeding skin-to-skin before she was bathed etc.). Anyway, the charge nurse there told me that OF COURSE they'd follow my birth plan, of course they do the AAP policy for breastfeeding, just be clear with the nurse about the birth plan and what we wanted when we arrived, etc. She acted offended that I even thought either would be an issue. So that reassured me; I knew I'd be bucking the norm but at least the charge nurse was supportive and knew what I was asking for was reasonable.
I've heard that at larger hospitals, the L&D nurses will often try to angle for their favorite type of patient - so a mother who is having a natural birth, or wants one, might get a nurse who is more supportive of that. Maybe.
Worth letting them know clearly when you first arrive! People here can help with your birth plan, too, incidentally.
I'd also look into a doula, as pps have suggested.
ETA: In practice, however, we did have a little issue. My OB had to stop the nurse from coming in to give the pitocin for active management of third stage of labor (placental delivery) - which would have meant that I couldn't do delayed clamping of the cord. Our OB was awesome, he stopped her in her tracks, told her I didn't want pitocin, that I'd noted that in my birth plan, that he hadn't asked for it, and to take it out of the room to dispose of it and it had better not show up on my bill either.
In her defense, I'd been at the hospital for about 20 minutes at that point and she hadn't really had time to look at my birth plan.