Anyway, as for Post-Crisis Clark, I am going to agree he was well short of Nu Clark. Post-Crisis I view him as being able to move the moon by himself, and the Earth with help, but he usually gets an assist from a GL to do it, who have know to do such things on their own anyway, so the feat isn't entirely clean. His history with celestial bodies has happened a bunch:
-Electro Clark used a magnetic trick to keep it up. Irrelevant.
-JLA/Titans crossover, the moon gets hijacked by weird alien stuff, and the JLA and company move it. While the moon seemed to be 2 or 3 times its normal size with all the alien stuff stuck to it, this does seem to be the lowest showing for Superman and crew.
- JLA story line, moon begins to fall towards the Earth. Kyle and Clark hold it up more or less indefinitely without issue, apparently starting out each holding a hide and then taking turns so the other could get a break.
- JLA: Terror Incognito, Clark, Diana, and Kyle treat the moon like a yo-yo, yanking it into Earth's atmosphere and then back out again and back in place, all in the space of a couple of seconds. It's actually a pretty insane showing. Either his top showing, or number 2.
-JLA Obsidian Age, Clark, Diana, and J'onn struggle to keep the Earth from flying out of orbit due massive oceanic disturbances. They might not have pulled this off, but they were saved at the last minute by Kyle, who pretty casually corrects the Earths orbit.
-JLA: Classified story line featuring the villain Starbreaker, who was using his power to pull the Earth out of orbit. Hal makes a giant harness, Clark puts it on, they proceed to out muscle the Earth from Starbreaker. This is probably his top end thing next to the moon yo-yo.
-Final issue of Final Crisis: Clark, a bunch of other Supermen, and some GLs move the planet. I need to recheck this for context, but I don't really think it is valid to use it try and marks Clark's strength. I mean, there are already a lot of showings of GLs, either as individuals or pairs, moving planets around. So it would be a low showing for them, at least. And it also could have been less "we need everyone to do this" and more "hey it would be easier if everyone helped out here." Also, weren't they pulling it out of some weird singularity thing Darkseid formed? Anyway, I don't think the feat is very useful for measurement purposes.