Briee, looks as if we made the same decisions regarding workouts and everything was fine! I'm afraid I don't know of any hard studies, but I can tell you the results of my own "research" at the time:
I asked my OB/GYN (a very smart, energetic lady in her early thirties who keeps up on the latest in the field) about the whole supine exercise thing. She said that in her opinion, it was OK for most women to lie on their backs for ab work or any other purpose. She said, "As you've noticed, I keep you on your back for your examinations, and you're there for quite a long time during ultrasounds." She said that if you're not dizzy or nauseated lying on your back, that means your circulation and the baby's are fine, and it is fine to workout or sleep on your back. If you are feeling dizzy or nauseated, then you may be compressing the vena cava and should come out of the exercise (if you're working out) or elevate the right hip (if you're just lying there -- e.g. put a pillow under it)
I also asked my pre-natal Yoga instructor, a very knowledgeable person with many years of experience. She told me that the advice not to lie on your back first came out about 10 years ago, with the book "What to Expect When You're Expecting". She felt that this book was fear-mongering, and found it pretty negative in general. She told me the same thing as my doctor -- basically, just trust your body. The human race survived just fine before this advice ever came out.
Finally, I checked with my mom. She had 4 kids. She slept on her back for all of us, as it was the only comfortable position for her. And she delivered on her back!
I also think that strong abdominal muscles are very important in pregnancy and delivery. I had absolutely no lower back problems, and I was able to maintain good posture -- I think that a lot of this was due to my abdominal and core strength (as well as traditional ab work, I did modified planks -- knees on floor and hands on step -- for most of my pregnancy) Plus, I bounced back very quickly after my C-section.
Anyway, sorry to go on and on. I also would be interested in seeing any hard facts or studies on the issue. Cathe and Sheila take the conservative approach on this issue (and I have the highest respect for both of them -- they are well-educated, experienced, and possess common sense), so possibly they could supply some leads?
Stebby