> the plate. Indeed it does but the whole thing (my totem-pole drivers with
> the 2N3904 - 2N3906 combo) generates far too much heat.

Not suprising, you have stored significant energy in the magnetic field of
those coils, and it MUST dissipate somewhere. If you don't provide a place
for it to go, it usually picks your driver transistors.

Depending on your driver (sounds like an H-Bridge) you may get away with
just a diode across each transistor.  Also, watch out with your switching
times. If you get both transistors on one side of the "H" on at the same
time (they don't just turn off when you tell them to) then you get
"punch-through" which makes for more heat.  Set up a variable off-time
between states, start large, and experiment with cutting it down. Applying a
scope with voltage and current probes will be an enlightening experience! :)
BTDT with stepper drivers, you just have one more channel to manage.

Depending on how you play your timings, you can leave the phase open, or
short it to dissipate the energy. Open will dump through the protection
diodes back into the supply, short will dump as heat in the transistors.