So, instead of using the built in signature, try using canned responses.
- Go to Labs and enable the Canned Responses lab. Save.
- Go to Settings, General and turn off your Signature. Save.
- Compose a new message and type your signature in the compose field.
- Click Canned Responses above the compose field and choose Save. Give it a name, such as "My Signature".
- Discard the message.
Now, whenever you want to include your signature in a message, just click Canned Responses and choose Insert My Signature.