I have a 98 standard with 11,000 miles. It runs great and I'm having no problems with the fuel petcock. I also have a 03 shadow spirit for my wife. I was starting the bikes yesterday since it finally got above freezing. I noticed that the fuel petcock for her bike was leaking. That model is not rebuildable.
You mentioned that the petcock is not rebuildable, so I take it that it is riveted together. Others on the HSATF (ACE T) have placed the petcock in a vise to compress the rivets some more, and others have drilled them out and replaced with a nut/bolt, both with success.
Since yours is leaking, you need to do something about that, replace it.
Doesn't the spirit have an electric fuel pump? So all would need is a shut off valve. My ACE T has an electric fuel pump, because the carbs are higher than the lowest point of the fuel tank, fuel needs to be pumped up.