One way to think of it (not too scientific) is that adding power just
adds more "juice" to the spin. The power vector rotates around, just
making the plane do whatever it's doing with that much more vigor.

I understand what you're trying to say, but I just can't get a handle on the
physics of it ...

Sure, I can understand how (without power) the aircraft would want to
continue rotating about it's centre of gravity (like a spinning top) - but
with power applied it would seem to me to want to accelerate the aircraft in
a given direction - which I would of thought would have initially increased
the distance from the centre of the spin to the centre of gravity (one and
the same with no power) to something bigger and bigger until control was
regained. In the case of a little power I could see how the aircraft might
continue to spin (perhaps to a point where the nose or some point further
forward becomes the spin center) - but with a LOT of power I would have
thought that eventually the aircraft would just start traveling in the
direction of the thrust (with less inclination to turn).

Obviously I'm wrong, but I just can't understand why adding say, 16,000 to
32,000 pounds thrust along a given line won't accelerate the aircraft away
from the centre of the spin.

I can only visualise it increasing the spin rate if the thrust was somehow
vectored 90 deg.

Where am I going wrong?

Cheers,

CC

PS: Thanks to the 2 other posters - I hadn't thought of decreased engine
power in the equasion, and I can appreciate how adding power in a
conventional spin maked things worse - it's just the flat spins / falling
leafs etc that have me baffled.