Heres a quick little explanation of how electricity works... A lower voltage going thru one coil will require a higher amperage than the second coil running a higher voltage. Both coils will not play exactly in time with each other. The coil with the higher power on it is going to have more control over cone movement than the other coil.
One coil will try to produce a note while the other coil is off time with it. Basically one coil is going to want to move one way when the other coil wants to move the other. This is just going to cause cancelation or muddy sound from the sub and its just going to eventually tear itself apart at the coils.
Only running one coil will basically do that same thing. The coil with no power on it is being rapidly passed back and forth across a strong magnet. This will also create a small amount of voltage on that coil. It basically works like the alternator in your car with a up and down motion instead of a rotational motion.
Either way that speaker will die eventually. Wait and see what happens to your amp when the 500 watt rms coil and the 125 watt rms coil short with each other. You're basically going to send the 500 watts from channels 3/4 back to your amp on channels 1/2. I'm sure the amp isn't going to like that much since its not strapable. I'm also pretty sure the amps built in protection isn't designed to take that large of a wattage on 2 channels that only put out 125 rms.
In the end you will probably have a blown sub and a worthless amp. I know I don't like to waste my money and this is a situation where a lot of money is going to be wasted.