Can you hoist a person up a mast at 60 degrees to the vertical,
without a capsize?

Well, with our imaginary boat w/ a 10m mast, 1.8m keel of
3000 lbs heeled so that the mast is flat on the water:
(roughly a 27-footer, pivot boint between mast and keel
in the center of the cabin, me on top of the mast.)

Mast side: 200 lbs person * 10m = 1000N * 10m = 10,000 Nm
Keel side: 3000 lbs Keel * 0.9m = 15,000N * 0.9m = 13,500 Nm

Give and take a bit with the approximations, I'd say you can
on a 27-footer if you are light and daring and for sure in
anything larger than that.

But then, in waves that tilt the boat 60 deg from vertical, I wouldn't
want to be hoisted to the mast. And I'm afraid that in the waves that
generate the ten housand ++ Nm to get the mast under water, the
1100 ft lb (is that approx. 1500 Nm?) mentioned in the next post
are rather inconsequential. Not that I've ever tried it.

Chris