A few questions: does the ceiling feel solid when you push on it, or is there some give to either side of the crack? Is there a way to examine the ceiling from above? I guess I'd want to know what's caused the crack before I would figure out how to repair it. Is there sagging joists? If the ceiling on either side of the crack is pulling away from the supporting lath, then you might have to do something to address that before actually dealing with the crack itself.

The ceiling is solid on either side of the crack. I can't check the ceiling from above (it's a sloped ceiling directly under the roofline). The ceiling all around it looks very secure and straight, no problems, so pulling away.

Well, that's good. The mesh tape is used to bridge a crack like that, so it would seem then that the person who previously fixed the crack was doing that properly. I've dealt with smaller, shorter cracks, and in those instances I widened the crack somewhat and scraped/cleaned it out in order to give the patching plaster a place to be spread in to. On those small cracks I didn't use the mesh, but just wet the crack with water, smoothed the patching plaster over the crack, and sanded smooth when dry. If it needed a second coat then I rewet the area, spread more on, and sanded again when dry.
The mesh seen in your photo sits atop the crack and was placed over wet patching plaster when applied, and then it's a matter of spreading more patching plaster over it in a wide enough area so that you can 'feather' it out more gradually and you don't get so much of a noticeable ridge or slope off the edges as is seen now. It appears, however, to be painted with a paint that has some level of sheen to it which I would think would interfere with any new plaster adhesion, so you may have to remove the paint in a sufficiently wide enough area on both sides of the crack and see if you can still work with the mesh that's there. If the mesh is disturbed too much or becomes frayed, you may have to take it off and redo it with new mesh. Just keep in mind that old plaster will not be perfect, and you do the best you can. There may be others here who can give you additional (or even better?) advice, but that's how I'd handle it.

My husband's really doesn't like the ridge, and the rest of the ceiling is so smooth he thinks trying to blend a 3/4" deep ridge will look obvious, so his tentative plan as of this evening is to remove the ridge of mesh to try to flatten it, then try to redo the crack repair smooth. It seems that the sagging part isn't an edge of the mesh, but is a center part of the mesh -- like an upside-down mini-mountain ridge. Should he try to cut out just the ridge part of the mesh with an exacto knife, or does he have to remove the whole mesh tape (even the part that's not sagging)? And should he re-repair the crack / removal damage with flat drywall tape and joint compound? Or is there something plaster-specific that he should use? I'm not familiar with the patching plaster you mentioned. We'll be painting over this after it's fixed.

sfsuperstar: "My husband's really doesn't like the ridge, and the rest of the ceiling is so smooth he thinks trying to blend a 3/4" deep ridge will look obvious, so his tentative plan as of this evening is to remove the ridge of mesh to try to flatten it, then try to redo the crack repair smooth."

That sounds reasonable. You may have to widen the crack just a bit more and clean it out, trying to cut under the edges as much as you can so the patching material has a place to grab in to and hang on.

sfsuperstar: "It seems that the sagging part isn't an edge of the mesh, but is a center part of the mesh -- like an upside-down mini-mountain ridge. Should he try to cut out just the ridge part of the mesh with an exacto knife, or does he have to remove the whole mesh tape (even the part that's not sagging)?'

I would guess it depends on how easily it cuts. I've not used it before, so I can't say. If it ravels and gets frayed and stringy, then it may be hard to cover over again with whatever you use.

sfsuperstar: "And should he re-repair the crack / removal damage with flat drywall tape and joint compound? Or is there something plaster-specific that he should use? I'm not familiar with the patching plaster you mentioned."

It may be OK to use the drywall tape, but I would wonder how much it would give or move under changes in temp and humidity in the ceiling without breaking loose at some point. I really don't know! We got the patching plaster at the hardware store; it's dry and comes in fairly small bags, and you just add it to a small amount of water in a container and let it absorb the water, stirring or 'folding' the mixture only very gently. If memory serves, drywall compound is still water soluble after it dries, while the patching plaster is a bit more impervious to water once it dries. Drywall compound also has a tendency to crack easily as it dries if it's applied to thickly, and the patching plaster doesn't do that as readily.

If you have a 3/4" ridge, you have more then a cosmetic issue. If you have a 3/4" gap, same thing. These two are different and have different structural origins.
You need to figure out the cause before you futz with the cosmetics.
Ron

One way to fix this plaster defect would be to remove all of the sagging and/or loose plaster, vacuum the underlying lath until it is reasonably clean, spray the wood-lath with tap water, and apply base coat plaster as needed. It will be necessary to dish the base coat plaster slightly, so that the resulting surface is below plane. After the base coat cures, finish coat plaster can be applied to bring the surface up to plane. The raw materials are inexpensive, less than 100 dollars total, and there is no great skill required to get a good quality repair on a linear crack that is less than six inches wide. Keep in mind, however, that if you begin removing plaster, and end up removing a larger area than anticipated, that you could end up with a repair job that is beyond your ability to complete. If this happens, you will either have to get skilled help, a tradesman, or resign yourself to a rather difficult learning curve.

Great, thanks for the tips. My husband removed the mesh tape that was sagging, and how we have a 1/2" deep trench about 3/4" wide and about 4 feet long where that huge sag of mesh used to be. It actually looks better already. The ceiling is sound, it was the mesh repair of a small long crack that was the problem. His plan is to try to re-repair it by filling the trench with joint compound, then taping and using joint compound to smooth over it. I'll let you know how it goes!

Use the powdered setting type compound and not the premixed stuff. The first one sets up similar to the plaster and the second one just dries out eventually.