Probably half of it is burnt out.

Like you said in your original post: This one's a poser. My thought is that if ypu have full voltage without the load, and half voltage with the load, the resistance of the load is the problem.

Sounds like you may have a house wiring problem.

Try flipping the breaker off/on slowly a couple times.
Sometimes you can loose half the line without actually tripping the breaker.
If this does nothing, check the voltage at the plug
L1 to L2 should be 240 volts
L1 to Neutral and L2 to Neutral, both should be 120 volts.
If OK
Unplug the unit and check the wires at the terminal strip in the machine to make sure none are loose or burned out
If OK
Check the power at the terminal strip.
Do this with the heater off and on.
[COLOR="Red"]Be careful as 240 volts is lethal !!! [/COLOR]

Do you have the wiring diagram.
It is a GE so it is not available off the net?

The reason I asked you to check at the terminal strip is that this is a very weird problem so am reaching for straws.

As you already know the heater 240 should have nothing to do with Neutral as it only uses the 240 legs so when it drops to 120, it seems to indicate that not only is it loosing one leg but it is also somehow getting the Neutral into the circuit.

Does it do this in both timed dry and auto modes?

Have you looked in the control console for the wiring diagram in the control console often they like to store the diagrams in there.

I am assuming that this unit used to run OK at this location even though you have not specifically said this. I just want to be sure this is the case because in the past I have gone in circles only to find out that the unit was new to a person and someone else had messed with the wiring.

Do you get any heat out of the heating element?
At 18 ohms the element should still act as an 800 watt heater.
Just wondering if perhaps this is ghost voltage but I would have thought it would drop to 0 volts. Again grasping at straws.

I think we can assume that there must be a resistance involved somewhere in this problem because if the Neutral was being switched directly onto one side of the heater then you would pop the breaker.

I can only see 2 parts that would be a resistance. The cycling thermostat (Item 263 in Section 7) has the heater contacts but also an internal heater.

I am not sure about this one as it is not listed but the parts show an Item 220 in Section 7, this looks like a resistor. My guess would be that it is used during auto modes to drop the 240 volts to 120 volts for the timer motor.
On many units the timer motor gets power through the heating coil when the heater is shut off by the main (cycling) thermostat.

I would remove the 2 smaller wires from the cycling thermostat. These should be the internal heater. The larger 2 are for the heating coil (Usually red). Then tape them up so they cannot short to the frame or each other.
Then plug it in and give it a try.
If this does nothing.
Remove one side of the resistor and again tape it up and give it a try.

Very, very weird.
I will do some searching for the wiring diagram it would come in handy here.