Good post, great pictures.
The truth of the situation is that all of the soft brass parts of a carb are considered (by the manufacturer) to be "consumable parts". It's a mindset that you have to embrace (and I realize doing this isn't easy, mostly because we want to believe our eyes and our eyes tell us "hey, this part looks fine!").
"Back in the day" of carbs, during a service or rebuild on a set of carbs that were no longer working well, it was just normal procedure to get the appropriate rebuild kit and replace all of those parts (the brass parts, springs, and anything made out of rubber such as gaskets and O-rings).
I'm not saying that any of your carb's brass parts are worn out, in those pictures your Main Jets and Emulsion Tubes look pretty good to me and they could all be within-spec and good-to-go. It's very possible that your Main Jets and Emulsion Tubes are not the real source of your problem.
So, because of this, I have to ask: What did you find when you disassembled the Pilot Jet system from your carbs?
The Pilot Jet system on these Mikuni BST ("Slingshot") carbs can be a problem. The Pilot Needle Jet Screw itself is tiny, and the fuel supply passageway through the body casting of the carb that feeds the Pilot Needle Jet Screw is the longest and most narrow passageway there is in the entire carb.
And... to make things even worse (and more prone to problems of a long-term, age-related nature) the BST Pilot Jet system has a very, very small rubber O-ring on the base of the Pilot Needle Jet Screw that is absolutely vital to proper operation. This tiny rubber O-ring has to provide an air-tight seal at the base of the Pilot Needle Jet Screw (where it screws into the carb body). If the base of the Pilot Needle Jet is not sealed air-tight it will not be able to make use of the vacuum pull that the carbs generate during cranking and low-RPM operation. This vacuum pull is critical because it (the vacuum effect) draws fuel up into and through the passageway from the carb bowl and through the Pilot Jet orifice. If there's no vacuum pull (or not enough vacuum pull) the Pilot Jet system won't move any fuel to the engine.
This would explain why you have to "crack the throttle" when starting the bike.
Obviously, I recognize that I'm now offering up my second theory of why your Bandit is so hard to start. But I'm just trying to help.
When you try to start the engine in colder-than-normal conditions the fuel delivery requirements are different. And if the Pilot Jet system isn't functioning due to either being clogged up or unable to pull fuel out of the Float Bowl, you will have to deliver the necessary amount of fuel by "cracking the throttle". But on a cold day your normal "crack" probably won't be enough to start the engine right up. So you probably end up "cracking" it too much which causes a flooded condition in one or more (or all) of the cylinders.