Spats, leveling as we are talking about refers to the rifle tilted to the right or left or the scope is "out of rotation" to use your words. Basically you need the crosshairs to point perfectly up and down and perfectly level to the right or left in order to keep the bullet from going to the right or left when you start dialing in elevation.
For your other comment about the scope being level front to back, this isn't really a thing. You can buy scope mounts that purposefully puts the objective lens (closest to the muzzle) lower. Most common example is a 20 MOA base. Basically what happens with a normal scope mount is that the scope runs out of adjustment to account for the extreme drop of the bullet at longer distance. The 20 MOA base right off the bat means you can get your crosshairs to aim 20 MOA lower. Or looked at another way, the 20 MOA base allows you to zero your rifle at 100 yards about 80 clicks closer to the top of it's adjustment range (assuming 1/4" per click @100 yards). As you get out to the really long distances, you have 80 more clicks of elevation you can dial in. Hope that makes sense.
I remember when long range shooting seemed almost magical to me. The crazy part is it's no where near as hard as I thought it would be. The exact same principles that helped me shoot small groups at 100 yards is the majority of shooting long distance (I'll caveat within 1000 yards). The hardware you're shooting likely has to be upgraded, but other than that it's mainly some math, learning to read ballistic tables and the wind. My uncle is responsible for this expensive past time of mine, and I really didn't believe him when he told me the problem was more my equipment than me. He was right! Of course this was in the days before The surprising level of accuracy you can get from guns like the Ruger American for cheap (I wasn't familiar with Savage back then.. I wish I had learned about them sooner). Now, even more so, reasonable accuracy at distance is very attainable with most budgets. And I say "reasonable" on purpose. Chasing smaller and smaller groups such as is required for competition shooting is a never-ending black hole of tweaking, testing and buying new reloading equipment. I can tell my desire for small groups is only so strong! Haha
There's something addictive about hearing that "gong" at 600+ yards. And imagine the confidence you have with a 300 yard shot on an animal when you can hit 600 yards 4 out of 5 times. I love long range shooting and hate that the closest 600 yard range is about 3 hours away from me. I've got 100 yards 30 minutes away and 200 yards an hour away. When I can find time to shoot, I normally go to the 200 yard range.