SGI, GI Player's distance irons, blade, player's irons, the golf OEM decide in which one their irons set belong...
A Ping GI could be a Mizuno player's distance... I would simply try a bunch of them first for the feel / look then would get fitted.
I think cobra F9 are Game improvement if I remember correctly, the Super game improvement are F-max.
I wouldn't really mind about the loft either and distance but more about the ability to hold green and distance consistency. I would hit bad shot also while getting fitted ON PURPOSE to see how they behave.
I play ping G425, everyone know when they hit a bad shot, I tend to be a little vocal about it when I do and half the time my ball end up very close to my target, my golf partner often tell me to shut the *** ** because my ball ended on the green, I didn't had a good height, wasn't a well struck ball but it still ended in a good place. Make sure the irons you get, whatever the category you try, that they still offer you some of that forgiveness from a GI / SGI.
If you like the Cobra king tour with MIM tech then by any means, get fit for those if you want, these are very good irons, great reviews overall including mygolfspy.