I shoot on all three DSLR formats, and find the 24-105 is least used on my 1.6 cropper. But I have the 17-40 to fall back on, just as you have the Tokina. Focal range apart, I think you'll be delighted with the results from the 24-105. There is some barrel distortion at the wide end, but nothing that can't be corrected in PP. Otherwise, a cracking lens.
And don't worry about ƒ4. There are some here who have an antipathy to that number, and I am sure they can quote in extremis examples where it's just not enough. But, given the cleanliness of high ISO on modern cameras, going up from 400 to 800 - or even 1600 - is no handicap. Higher than that, and you want to be considering flash. Flash is banned? OK, one of those extreme circumstances. And, assuming no subject motion, the IS will handle 1/15 just as well as 1/30.
If you're talking a hyperactive black cat in an unlit coal cellar, well, you're screwed. But so you would be with any 2.8.