My OB defers to my MFM always.
Can you call the MFM office and tell them this issue? Maybe if the MFM puts something in writing recommending delivery at 37 weeks, the OB will agree, or has that already been done? (My MFM is good about putting important stuff in writing for my OB.) It would be a bit risky of an ob to disregard an mfm's rec like that, liability-wise, I can't imagine that they would.
A bpp can't really show the baby is ready now for delivery. It can show that the baby is doing well or not doing well in there (and if baby's not doing well, that could be a reason to deliver asap.) And it can give you a general idea of the baby's size, but that's the limit. You could ask for an amnio for lung maturity if that would help convince them to deliver (practice breathing in a bpp does not guarantee lung maturity, it's just a good indication baby is not in distress. A good amnio score does pretty much guarantee it.)
Me (29) DH (30)
#1-Olivia Caetlyn-9-28-09-9-28-09, 23+2 wks, emergency classic c-section, class I HELLP, IUGR
#2- Lucas Oliver (rainbow baby)- April 2011, 36+2 wks, HELLP and pre-e free! (lovenox and LDA pregnancy)
#3-Matthew, late October 2012...mostly normal, 37 wks, (lovenox and LDA again)
My blog: http://www.butterflies-and-rainbows.blogspot.com/