That's not "girth", that's diameter or width or, in this instance, thickness. Girth is the same as circumference. And 2.2" circumference is about 3/4 of an inch thick.
6" circumference is 1.9" thick. So that 2.2" wide tube will work.But that's also the limit you'll get in width increases since you may be touching the sidewall soon enough. If there's a size one step up, you might consider getting that one.
I have the X30, myself.