I'm willing to bet there is nothing at all wrong with your sub.
A short in your sub is certainly a possibility but a ground loop interference is more likely what is happening here. The steps you've taken so far have not done anything to rule out Ground Loop Interference (GLI).
No, I don't think that is a good assumption. If a GLI is dominating your LFE input then it why wouldn't a GLI problem effect bass response? Of course it would. Especially if it is a loud humm.
This test would lead me to suspect a GLI problem when using the 3 pronged sub. The reason your Paradigm has no GLI problem is solely because it has no ground connection. A 3-2 (cheater plug) plug eliminates the ground circuit from your sub which will identify a ground loop issue if there actually is one but we still don't know since you haven't tried that yet. Connecting your 2 pronged Paradigm sub is not going to identify a ground loop interference even though a music signal is successfully passing through your LFE output.
The Paradigm is designed with no ground wire to avoid GLI issues. With no ground wire there can be no GLI issues even when a grounded sub indicates a GLI problem. If there is a GLI issue with a sub, the sub is not to blame. The signal to the sub is at fault and is often caused by the cable company using a different ground system than the house wiring circuit. Elminating either the house ground or the cable ground will usually eliminate the humm. Also try completely disconnecting the cable from the system.
Unfortunately the higher-end circuitry in the Descent requires a ground so it can function when using the balanced input. I'm hoping the new Descent i and Depth i have solved GLI conflicts with thier new circuits.
Until you spend $2 and 2 minutes to try the cheater plug test and/or disconnect the cable from the system you won't know if it is simply a bad case of GLI or not.
I have to agree with you on your statement.