Electrum client for Android doesn't have the feature to signed a message with your address, you can do it only on Desktop version of electrum, but if you are an android user I will suggest that use Mycelium mobile wallet, it does have the feature to signed message on any wallet address there, the one you created which is HD wallet and even the imported one but not the watched address.
No problem using Mycelium (wish they used the same word list as the Electrum version I used to create my wallet, though), but how do I get my private key out of Electrum on Android?
When you make a wallet, you get a seed.
You can use this seed to get the private keys and master public key. This seed can be input in the desktop version downloadable here
hereUhm..., did you read what I wrote? I have no access whatsoever to any desktop version of Electrum. I need to get the private key out of the Android version.
Electrum wallet for Android is limited. You can't export private keys, and since Electrum uses a non standard derivation path you cannot restore the seed to another Android wallet like Mycelium. So find a laptop you can install Electrum on and restore the seed as you will never be able to do what you want with the Android version.