As for 305/45-22 fitting and not rubbing, tough to say?
Will probably depend on how your truck sits, the offset of the wheel, which I imagine there's not a hell of a lot of leeway as far as offset goes on these vehicles without problems rearing their head. One is probably only able to play with a few millimeters one way or another.
In a thread I started down in the older Tahoe section of this forum, I myself am currently looking at a set on another person's 2005 Yukon Denali, the wheels are 22x9.5, I gather have a +30mm offset, and Nitto NT420S 305/40-22 Tires are on board.
And I did notice some slight rub on the outer plastic fender trim on their vehicle, not bad, but there none the less.
This has me concerned, even though my '97 Tahoe I believe sits higher than their Denali, height I realize will not be just the only consideration, and thing to worry about that can cause rubbing-contact.
I'm worried about the much wider tire, and of course the offset of the wheel. For sure I don't want the inside of the tire hitting suspension components, or inside of the inner fenderwell, nor do I wish for the outside of the tire to come in contact with the Fender Lip.
Without any lift on my truck, even if under normal conditions I do not get rub, I'm still worried and concerned about entering parking lots, or a possible off road scenario where the suspension goes through full travel.
Without trying such on the front of my truck (doubt the back would ever be a problem), I just honestly don't know at such point with my own vehicle. I surely wouldn't wish to screw my mint truck up just for a "a look".
With a 305/45-22, I suspect these tires will even be a bit taller yet by a few tenths/inch than a 305/40-22.
Not sure if this helps you any?
Mark