Do I really need to stud nail all the crown molding

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.

What is important when nailing crown molding is hitting a solid background. This can be plates for small crowns or studs. What I prefer to do is add a profile (triangle) piece of scrap wood, such as mitered plywood or ripped 2X4 stock into the corner and nail it into the plates and studs. No problem if you miss or have to use a lot of nails to find a good solid backer because it will be covered by the crown. Now when you go to nail the crown, you will have a good nailer everywhere. I usually use nails along the top edge down 1/2 inch from edge and same along the bottom edge. This helps close any gaps along the ceiling and wall. You can go back after and fill any gaps with painters caulk and touch up to match the crown (if painted) or the wall/ceiling colors respectively.