jerseydevil, running without an airfilter for any amount of time, esp in dusty conditions is not good. I would guess that the saw was running too lean (too much air relative to gas). This will cause the saw to get too hot, score (somtimes actually melt) the piston & cylinder near the exhaust port -- this in addition to wearing out the engine just from all of the dirt that got sucked into it. In addition to cleaning all the junk out of the carb, I would take the muffluer off & pear into the exhaust port. If you pull the starter you will see the piston move up & down through the port. Does it look shiney, scrached, melted? If it does, dont waste any more time. Take it back (again) before the warranty is out. If this is the saw's second rebuild, the cylinder walls are probably very beat up. They really should give you a new saw (a new cylinder is usually nearly as expensive as a whole saw).
If it were me, I'd try for a refund on the Craftsman, or at least peddal it for whatever you can get for it on ebay (do be honest in the description). My favorite cheap (but worthwhile) saw is the stihl 210. About $219 w/ 16" bar. Its 2hp, 35cc compared to your 200T's 2.2hp. Cant go wrong with the 290/310/390 if you want more power, for a reasonable price. The 290 will pul a 20" & is just a bit north of $300. I run an 039 for bucking and 021 for limbing (older models of the 210 & 390) they serve me well.
I dont know much about Stihl electric saws. Stihl usually has good stuff & will stand behind it with service & parts. That said, I would guess you may have fewer problems with the cheapie electric saw than the cheapie gas ones. Personally I'd want 2 gas saws. That way you have a backup when your "in the field" harvesting your firewood.
After reading this post, I can't help but to throw my $0.02 on craftsman stuff. I like the hand tools. The powertools are usually OK for the price, but no where near as good as Makita, DeWalt, Milwakee. Sears lawn & garden stuff are almost always trouble.