That doesn't look like varnish to me - looks like sealant on the welch plug. The carb looks rather clean actually. I suspect it's a wild goose chase.
What has been done to the saw? Did you remove the limiters or did someone else, and if it was someone else are you sure what all was done?
Have you checked the metering lever height yet? That is a likely explanation of the issue, as is damaged A/V mounts or a boot given that it's been pinched and yanked on.
Last, it sounds like it has been lean at times in the past, so you should pull the muffler and check the piston. Low compression will make it hard to tune and lazy.