I would adjust the carburetor correctly BEFORE doing any cutting. If you don't add some fuel the damage will only get worse.
From the description, the P/C should be OK, may not need any parts, just taken down and cleaned up to make sure there isn't any piston material smeared over the ring and on the liner.
Don't be afraid of ethanol, never had the first problem one with it. Just use good Husqvarna or Stihl premium mix, and set the carburetor so it is delivering PLENTY of fuel at full load.
The saw should "four stroke" at no load, then clean up nicely in the cut. Some Echo's have a rev limiter or high speed timing retard module built into the coil, and can be difficult to set. I'd go plenty "rich" with the "H" speed screw, till power falls off, then lean it up a little at time for the best power in the cut at the richest setting(s)......Cliff