Not at all, in fact the 22.5" model typically is even easier to fit the cover on when using a hinge, compared to the 18.5" model.
The factory cover should have no issues. Sure, it has to stretch a tad, but the elastic shouldn't be "maxed" out and you shouldn't have to use an excessive amount of force to get it on (though those covers are a tad tricky/slippery in the first place).
Unfortunately, since the hinge is a 3rd party product, if you continue to have issues, Weber won't be able to help you. I just can't imagine that it won't fit though. I don't think anybody's ever had any issues with 22's.