What is your pilot air screw set at? Have you pulled the plug on the carb blocking this screw and tried to adjust it?
You see, it is supposed to be set at about 1 turn out from lightly seated, but most of us have found the sweet spot to be around 2.5 turns out. Another reason I mention it is because someone recently had a new TW and the screw was all of the way in! So, it's something to check. Good luck to you.
p.s. It's a low compression engine that runs best on good ol' 87 octane, and that's usually what I recommend, however many stations now are offering ethanol-free super, in which case that is a good way to go. This should not matter with your above issues, I just thought I'd mention it.