this will be a good question for the code experts...
In my opinon, the 3 prong solution (while it met code in the old days)
is very dangerous and I would not go backwards to it.
It is dangerous becasue if a fault should develop in the wiring such
that you had an OPEN circuit for the neutral/ground, you could get
120Volts on the metal cabinet of the dryer which is obviously very
dangerous. This is one of those crazy cases where something meets code
but is still very dangerous.
My suggestion would be to change your house outlet to a 4 prong outlet
and find out the code approved method of getting a saftey ground
connection for the 4th prong. Maybe you can wire it to a nearby 120
Volt outlet that has a saftey ground. Here is where the code guys can
help by telling us the code accepted way of doing this.
If code says that you have to leave the 4th saftey ground pin not
connected and add a label to the outlet warning that it is not
grounded, then I would do it that way to be legal. But I would connect
another wire from the dreyer cabinet to the saftey ground on a nearby
120 Volt outlet to make it safe.
Bottom line is you want the dreyer cabinet to be connected to saftey
ground only, not to neutral.
Maybe there is a 240 Volt GFI? Anybody know?