I also just got a phazer, 2012 mtx, and it had very similar issues. the guy i got it from, got it in offseason last year and had done alot of "garage starts" and shutting it off right away. I pulled the spark plugs and they were black and fouled as can be. These will foul easily if you start and do not let warm up before shutting off from what i have read and experienced early on, once you start do not touch the throttle until after it lowers from its warm up RPM (2500 i think) down to it's normal idle of 1800.
After i replaced the spark plugs it started right away and went through its idle sequence perfect for the 3 days in a row i checked it. What i did when starting it (knowing i would not be able to ride it) is after it warmed up and idled for a bit, i would rev it up just to point of clutch activation a few times before shutting it off and that seems to have worked for me to avoid fouling the plugs. (i am very much a newbie so not saying that is recommended, just something i found worked to prevent the fouling of plugs during "garage starts")
Start simple and replace the plugs, i was worried a little bit about mine too and once i replaced the plugs it eased my worries. Now just wait for some snow to find out.
Just to be safe i also drained all the gas out of the tank and filled up with fresh fuel and added a bottle of seafoam.