The thing that could be harmful in this situation would be this: You turn the
motor off, and as it slows down, the starting windings kick in. If you chose
to reenergize the windings for reverse rotation before it stops completely,
the motor would draw higher than normal starting current.

Leo, I don't see how this is so. Even if it did draw more to overcome stopping
and then reversing (which I doubt), it would be a small increment because by the
time a 1725 rpm motor's starting circuitry could kick in it's rpm would be down
to about 2-300 rpm. That's not a lot of torque to overcome.

And, my experience with reversing a motor that uses starter circuitry is that it
must be at 0 rpm otherwise the motor just spins back up in the same old
direction, making it a moot point anyway.

Finally, I have yet to have a problem with reversing such a motor including one
connected to a very massive 18" sanding wheel. The 1.5 Hp motor takes about 5
seconds to get it up to speed. That's a large starting torque by anyone's
measure. And I've flipped that reversing switch at all rpms until I learned that
it needed to coast to a stop first. Not once did the thermal switch open or the
'magic smoke' leave the motor.

I've worked in factories and shops all my life and I have yet to replace a motor
because it was reversed improperly or too often.

Unless someone can come up with a significant history or evidence of what you
are talking about I'm just going to write this off as something for Mythbusters
to call 'busted!'

Dan