It's always a scary time at the end when those little suckers inside us don't want to corporate.
I did those exercises too, attempting to talk them into getting their head down. (both of mine were heads up till the very end and then moved) On my next visit, he was sideways, and on my next visit, his head was pointing at my hip bone and by the time my water broke, he was pointed down. Most of the time they move down on their own and you will not need them turned. Interesting that your Dr wants the baby head down at 37 weeks, it should be down, but they normally wait till the very last week to do it, if they need to turn.
Do whatever your Dr. wants you too, if you feel it's right. If you want to give the baby more time to move on his/her own, say it to the Dr. and don't be shy. (if you are already dilated to say a 3, I could see why the Dr wants to do it now, you likely won't go to 40 weeks, I'm sure she has her reasons, be sure to ask before you do it, remember it is your body.)
Also, if you are wearing one of those "support" belts, STOP, and if you are wearing the low cut jeans, STOP. Don't wear anything that will constrict that area. On my second one, I was wearing the support belt while I worked during the week, on a weekend I felt her move down, I could feel it plain as day. Then on Monday, put the belt on and up she went almost immediately, felt like a washing machine was turned on inside me. HA. I never wore it again, she dropped and I had her within one week. Just some ideas, hope it helps.
Good luck and I'm praying (everyone should too) for your baby to drop. There is no need for any more pain than you have to go through. God Bless.