En route to a fly-in this morning I started to notice a significant decrease in power with any reduction in throttle from full power. After applying carb heat, I noticed an immediate increase in power. This seemed to indicated carb ice to me (even though the temp is was about 90, dew point about 80-85). I made the decision to turn back to my home strip, and climbed to about 4K MSL. The power issue persisted for the remainder of the flight. When I reached my airport, I was forced to make a slow spiral descent at full power, until i reached an acceptable altitude for final. On final, i maintained full throttle until I had the field made, at which point I started to reduce power. This caused erratic jumps in power from idle all the way to full. I then cut the mags to stop the issue, which did not immediately result in engine shutdown. Finally after 30-60 seconds the engine shut off and I was able to safely come to a stop. It's a 47 J-3 Cub, original a-65-8, as close to stock as can be. The only variable is that I ran ethanol free car gas (93 oct) this morning, rather than Avgas, which I almost never do. Anyone have insight into what happened here? To me it was indicative of icing, but then the shut-off issue doesn't jive. Any help is greatly appreciated.