Drywall over irregularly spaced studs – how to secure edges

I know this isn't the answer you want to hear, but I don't think priming and painting will hide the tape.

Before you apply any more primer, I'd add another thicker coat of mud. Slather on the mud thick first - it doesn't have to be smooth. Then smooth it out by angling your 12" knife so it's almost parallel with the drywall as you drag it along the surface. You'll have to press fairly firmly in order to avoid air gaps appearing in the thick coat you're smoothing out.

You may have to get a feel for it. If you push too hard and can see the tape again, redo that section until you get it just right.

Wait for the thicker coat to dry, then sand the edges as smooth as you can get them. Very carefully/lightly sand over area covering the tape if you didn't get it quite smooth. You may need to do a second coat along both sides of the thicker coat to make it join the drywall surface smoothly.

Go ahead and place the drywall over the top edge of the crown moulding. Sounds like the wall was already re-plastered with it in place. If you tried to remove it, you may end up re-doing the walls as well. Even forgetting that, it's almost impossible to remove moulding without sustaining some loss. Without replacement material available, removal with intents of preservation is extremely risky, especially with stain grade material. You don't want to go there.

If your joists were flat, you'd still only need to shim down the first 4 feet or so along the walls, no one will see the resulting slight slope. Keep this in mind when planning your shims. It doesn't have to be perfectly flat, unless that gives you pleasure. You also don't need to shim to completely fill the gap. An 1/8" gap makes a clean shadow line that is not detrimental (assuming it is perfectly uniform) at all. It also makes finishing easier. The taped joints of drywall are normally not perfectly flat, despite the tapered edges. There is a slight bulge which is usually invisible. But against straight moulding, depending on the profile, this bulge may be visible. You might consider grinding down the edge tapers at the board corners against the wall so the joint tape can be completely buried and the yet the joint against the moulding can still be perfectly flat.