OK, we already know that the lug that's touching the edge of the barrel itself is ground.
to find the hot lug, plug the jack into an amp, then use a little metal wrench or screwdriver to touch each lug; the one that makes the loud buzzing noise is the hot lug.
one of the two leftover lugs will be for the negative from the battery; i have a feeling the two jacks are a switched jack to ground and a ring connection for stereo operation. you'd need a meter to tell, but i suspect that they would actually both work as the 9V negative.