Thanks to all who responded to my petcock post the other day.
I ended up ordering a new petcock ($120) last week, but it did not come in before the weekend. I decided to figure out what was causing the leak. I had a rebuild kit that I had ordered a couple of years ago so I went ahead and installed it. The old diaphragm looked good so I was skeptical that this was going to solve my problem.....and it didn't; the petcock still leaked pretty badly. I set the tank on the patio table, filled it with gas and finally found where the leak was coming from.

I got this idea from Pharmboy (Jim Lynch) since he told me that he did something similar to his petcock. I drilled out the rivets which held on the plate for the shutoff valve. Once I removed the plate, it was obvious that the gasket inside would have to fail eventually.

I then filed down the rivets until they were flush with the petcock housing, then drilled and tapped the holes to use the screws that came with the rebuilt kit that I did not need. I used a M4 x 0.7 tap.

I then used some gasket material to make a gasket, and used some locktite on the screws when I reassembled the petcock. No more leak!
