I'm voting with Mr. Mann, so that's 2 to 1.

Your mass and your volume will be the same if your lung volume is the same (and it's the same day, so you haven't gained or lost weight!). I think you could take a deep breath and relax into a cannonball float quite comfortably. How easy do you find it to float on your front vs your back? Your actual surface area is the same regardless of your position, since you're not going to cannonball tightly enough to actually include or exclude any water or air with your body, as compared with flat floating. I think your buoyancy just relates to an amount of water displaced, based on your mass and volume, so that shouldn't change. But you can ask Mr. Mann about that - I know more biology and chemistry than physics. Based on my experience with floating, though, I think the sensation feels quite different for the 3 floats; and this is probably the reason for your different experiences.

Give my greetings to Mr. Mann and tell him I think teaching high school science is a really valuable job. Also - check out 'buoyancy' and 'floating' and such on www.google.com - I think everyone floats, but maybe some people have too little fat, except in their heads, where our brains are full of fat. And try some simple experiments, too.

There are, of course, clay boats and foil boats, where you can displace enough water to make heavy things float, but I don't think that's what's happening with you.

Let me know if you come up with any convincing evidence that Mr. Mann and I are wrong!