How to tell if the sagging in the plaster ceiling is getting worse

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.

There is a strong chance that what you see is drywall overlaid a plaster wall. Plaster, does not sag or bow out as it is shown in your picture, not without severe cracking. Plaster is very brittle and does not take well to any movement at all.

Based only on what the picture shows, the plaster did move, or cracked or fell off or something like that. The remedy that somebody thought of, which is done a lot, is overlay the wall with drywall, whether it be 1/4" thick or thicker.

Flat window trim in homes the age your is typically very thick, 3/4"-7/8" thick, unless it was redone with newer stock. Regardless, the trim's edge is covered to a degree by the wall material, suggesting an overlay of drywall over the plaster.

To answer your question, since the base is already off, so it appears, cut the offending section out to the original wall surface, remove whatever is creating the waves in the wall and re-shim if needed and reinstall the same thickness of new drywall that was removed. It will still cover the trim to a degree, but it will be uniform.