Try alternating between the dog and cat yoga poses. There are videos on YouTube to show you how. That's how I got my baby to turn off of my back. It might work for transverse as well. Not sure, but it's worth a shot and feels good on your back as an extra bonus.
Yes they'll check me in the morning before they start anything. But they didn't think the chances were very good of him moving.
I don't have experience here so I cannot offer any advice but can give my best wishes! Will they do an ultrasound before sending you to the OR? Babies can flip, even in labor.