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.
A classic approach in cabinetry is the use of filler strips. These are pieces of wood, matched to the finish of the cabinets that are used to fill gaps, usually between cabinets. Often the horizontal spacing does not work out to exactly the width of standard cabinets (especially in renovation work). You design to the standard sizes slightly narrower than the overall, and then add a vertical filler strip between, or at the end of a cabinet, to fill the gap.
The same principal can be used to fill a gap between the top of the cabinet and the ceiling that will then give you a horizontal surface to attach the crown molding. A strip will probably have to be tapered to fill much of the gap, but it does not have to come down to a point because the molding will cover much of the gap. The strip can be glued into place,since it is purely cosmetic, but be careful when nailing in the crown.
The biggest question will be finish. If the cabinets are painted, you may be able to buy a filler strip from the cabinet manufacturer and run it horizontally instead of vertically.
For stained cabinets, you can do the same, but the grain will run perpendicular to that of the cabinets. It is a matter of taste as to whether that is acceptable to you.
You also could put in a homemade filler strip (plywood, clear poplar, mdf) and paint it to match either the cabinets or the the crown molding. If yo paint it to match the crown, the effect will be that the crown looks like it is a bit deeper at that point, but probably will not be noticeable.
Best Answer
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.