I don't think Weber makes all the covers the same. I've read numerous posts where some slide on with no problem and some that have a bear of a time putting it on, and that's without handles..
I did mine just like my OTG and they stand out 2 1/4" per side and my cover still fit,tho snug. I used to slide a large trash bag over it first and that made it easier. (less friction)
But I gave away my cover cause all my Weby's are garage kept. Personally I would rather have handles, and if the stock cover doesn't fit, try to find something bigger.
Tim