I birthed both from a supported back position similar to what you have described. After everything I had read between DD1 and DD2, I tried with DD2 some other positions (hands and knees, squatting) but just couldn't get comfortable so went with what I knew I liked. I think you should always go with what you feel even if it is against what is usually most effective, you know your body best.

For what it is worth, they were both positive experiences - spontaneous, drug free labours with no tearing or stitches. I did have a small graze with DD1 but that was as she had her hand up next to her head.