By "coved", do you mean the ceiling is a curved surface?

I deal with asbestos solutions quite frequently. You can get 1/4" thick drywall at the Home Depot and install it directly over the textured surface. It will mash the texture down as you set the screws, creating a nice smooth surface. Just mark out the ceiling joists and you're ready to go. Then tape and finish it like a new drywall installation. The 1/4" thickness drywall is best for ceilings because it is lightweight and you have to be careful of adding too much weight to a ceiling.

Thank you aidan_m, I'll try taking a picture of the ceiling tonight. The best way I can describe it is that the ceiling itself is flat, but the corners where the wall meets the ceiling curve DOWN from the ceiling vs. being at a 90 degree angle.

How old is the house, when was it built? I've seen these coved wall/ceilings in older homes in San Francisco. You may be dealing with plaster. Can you push a thumb tack into the wall without a hammer? I don't know about installing a layer of drywall over plaster. Not to say it won't work, I just haven't done it before. Maybe someone else has?

Have you actually had the texture sampled and tested for asbestos? The tests are not too expensive. Asbestos is safe as long as it is not turned into dust. There are very simple methods to safely remove "non-friable" asbestos containing material. Friable means the material easily turns into dust when handled. Wall and ceiling texture is almost always non-friable and only about 1% or less asbestos. Don't mess with friable asbestos or surfacing materials containing more than a few percent asbestos. The next thing to know about asbestos is water prevents the fibers from going airborne. Use a spray mister or Hudson sprayer full of water to wet the material prior to removal and continuously during removal. I use a second person manning the spray rig to keep the material wet. Only use hand scrapers, drywall taping knives, no power tools. Power tools create dust. Lay out 6 mil poly plastic all over the entire room floor and perimeter walls. Duct tape all seams, especially at the doorway to other parts of the house. Wear rubber gloves and put covers over your shoes. Best practice would be to have a bag under the scraper to catch the texture before it falls to the floor. Even though you put down plastic, you really don't want to track it around, even inside your little containment room. Dispose of the plastic and material in a large 6-mil poly plastic bag, with the bag twisted, "goose-necked" and sealed with duct tape. Mist plenty of water inside the bag before taping it up. Call the local landfills to make sure they will accept this type of waste.