Yes, it is choked.
I choke it and hit the start button and it will start up for a couple of seconds and dies... I have to help it out a little bit until it can idle on its own.
If that is all the issue is, you needing to "help it out" until the bike warms up and idles on it's own, then your choke, choke cable , or enrichment jet needs adjusting or cleaning.
If the bike runs fine once it is warmed up, it would not be gas. Although "winter gas" is crappier than "summer" gas due to additives.
I'd check to see if the choke is opening all the way, add some seafoam to the tank and not really worry about it if you do know HOW to start the bike when it is cold.
Because you did the earshave and it's always possible your jetting is not perfect. How many miles is on the engine, what brand/weight of oil do you have in it, and the condition of the gas all could make a difference too.
And water does sink in gas but not like a rock...it is as easy as pulling the bike up off the sidestand to make it "spread out" into the gas in the tank and enter the petcock tube.
We did this as an experiment once using blue dyed water and fuel in a small glass tank. The blue water would settle at the bottom, but if you tried to pick up the tank carefully and move it to another spot, the water would swirl up before settling down again.
You can not fill a tank all the way up easily, there will always be air pockets. I'm not sure you have any water in your tank, but if you did, the exact same thing you decribed could occur.
What size pilot jets did you install? Are you using iridium plugs?