The symptoms you describe(progressive backfire and then engine cutoff) and the mileage (6k) suggest a cracked vacuum hose going to the petkock. It costs $3 to replace with about 18 inches of fuel hose.
To rule this out, put the petkock on 'prime' and block off the vacuum nipple on the right hand side of the carb.
Leaking oil around the head gasket at 6k miles? 6k miles is about how long the head plug will last. (i know mine will start leaking next at 18k miles after resealing it at 6k and 12k). Symptoms of a head plug leak are: oil marks at the front of the engine below the exhaust port, and then wraps around to the left side of the bike. It will soil your left hand side cover. Block out a Saturday afternoon to replace/reseal this. This is also a good time to re-torque the heads and set the valve lash. Getting the gas tank off is the trickiest part of this job
Once you knock these problems out and mount your own tires(which are probably also due at 6k), you will become a certified Savage owner