[jhv48]

Is the advance curve on the distributor smooth?

Could be a sticking advance, but my bet is on the carb. You've got a single plane manifold which is "better" at higher rpm but that carb is my bet.

You can fart around all day long with that carb and it will run better, but will never run right. Ditch it for a mechanical secondary carb. Even Edelbrock will tell you that this carb is not the best choice for a light 5 speed Cobra.

My first Cobra had that Ed carb. Tuner was able to eliminate the problem you are having but the car would sputter on hard turns and almost die at hard stops. I replaced with a Speed Demon and never looked back.

Backfiring through the exhaust is probably a blown side pipe gasket. Try tightening them first. If doesn't go away, replace both sidepipe gaskets and hope it goes away. If it doesn't, check the exhaust manifold bolts for tightness.