Bob, I think you're absolutely right on the blades being dull. And yes, on the blade that broke I was not only pushing too hard but had tightened the saw too much. Luckily the blade broke and not the saw.
Until this thread I had never thought about sharpening those little tiny teeth. But why not, they're saws like any other saw. I'll be giving that a try later tonight.
Dave, using a drawknife to remove big blocks of wood is another possibility, however it might get tricky trying to do the deeper curves at the ankle and knee.
And George, of course my arm is pistoning at bandsaw speeds. That's why I was getting so overheated after 10 minutes of sawing.