You've done work on carburation, the ignition system, spark and timing, replaced the cylinder and piston and plug. I'm assuming the exhaust too.
At this point, you've eliminated all the usual suspects, so I'm somewhat at a loss as to what else could be wrong. (you probably are too)
The only thing I can think of at this point is a primary compression issue. But... you've already done everything possible with the cylinder, so you've probably resealed everything already. Recently there was someone on the forum who had a machine that refused to start. It had great (secondary) compression and no trouble with the spark or fuel. I believe he had a blown out base gasket and that was the whole problem. If you have the ability to, do a leak-down test on the trimmer. This will tell you if there is a massive leak somewhere, or the oil seals are faulty.
My memory is a bit fuzzy, but aren't these stihl trimmers a "triple decker clamshell"? I've worked on other machines that have the same setup. From experience, the base can leak from time to time, and needs to be resealed. I've seen them run weird, but I've never seen it so bad to where it won't start. I'm not saying this is the problem, just a possibility.
Make sure it isn't a simple problem or mistake that tunnel vision and frustration made you overlook. It's a royal pain, but you must check everything you've done and make sure it is correct. Clear your mind and focus... Make a checklist on paper or in your head and go from there.