Any reasonably powerful god could make a non-Euclidean spacetime in which the points equidistant from a central point also form 4 straight line segments of equal length that meet at right angles.
I also think the classic rock so heavy it can’t be lifted fails, for the same reason that an omnipotent god could clearly commit suicide, if it wanted to (and once it did, it would no longer have the capability to perform other actions).
The omniscience thing is harder, because of things like incompleteness theorem, but I don’t think I can really describe what it means to know everything in the first place. “Able to provide a true, and comprehensive answer to any question for which a true, and comprehensive answer is possible” doesn’t seem to give any contradictions, but as you mention has the feel of dancing around all the hard issues.
When I was in college, our sportsball team won a game against the other guy’s sportsball team by not many points. Many hundreds of students started a chant going out of the sportsball arena, and four freshmen decided to light a couch on fire, apparently thinking they’d just blend in. The police were there immediately, firefighters put out the couch in a few minutes, and they all got hit with fines.
In short, I think you’re exactly right, and most sportsball fans just want to be loud and drink.