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.
It sounds like you have a fixture controlled by a conventional dimmer and are using CFL non-dimmable bulbs.
Standard dimmers were designed for incandescent bulbs. Many CFL and LED bulbs are non-dimmable. Some are dimmable, but only work with special dimmers designed for their electronic circuitry (conventional bulbs have no circuitry, only simple filaments). Some CFL or LED (not many) will work with a standard dimmer.
First you need to make sure the bulbs are dimmable, and then that you have a compatible dimmer.
In general, CFL and LED bulb packages indicate whether they are dimmable or not. If it does not say dimmable, it is probably not. Dimmers also indicate whether they are intended for CFL and/or LED bulbs. Again, if it doesn't mention CFL or LED, it is probably not compatible, unless you have bulbs that specifically say works with standard (or conventional) dimmers.
Check the fixture by using an incandescent bulb. If it works, either go with incandescent, find CFL or LED bulbs that work with standard dimmers or swap out the dimmer.
If the incandescent doesn't work, you have a wiring problem or a defective fixture.
Best Answer
Have you de-nailed the molding yet? If not, pull the nails through from the backside. It will leave the finish intact.
If you marked the crown so it goes back up in the same place as before, you may be able to use the old nail locations to re-nail it to the framing. If the holes are not visible since the nails may have been pulled from the backside of the trim, use blue tape to locate them on the face to see where to nail. Piloting is a good idea too.
I have even used a larger nail pushed through the original nail hole so the larger finish nail head grabs the wood still. For example if the trim is nailed with 2 1/2" nails (8D) re-nail it with a 3" (10D) or 12D nail (3 1/4").