Can a new ceiling be build directly onto an old one
Adding a new drywall ceiling over an old bad, but solid surface is very common.  Looking at your question, the only part of your plan I question is the use of 2X4 strapping. 

I understand the need to add some extra insulation, however sandwiching it between the two layers of ceiling may not be the best idea. I'd rather you consider installing the extra insulation over the top of the old ceiling. Blow in some cellulose or roll some fiberglass batts would be a good option. There are a couple of reasons.

First; using 2X4's will lower your ceiling height an extra 3 1/2 inches if they are installed vertically to create a 3 1/2 gap for insulation. You may find it very difficult to level and attach them. You would have to use very long screws.

Second; although I don't think it would be a moisture trap for normal migration, it would be a horror show if for any reason you had a leak from above. Any water that would penetrate the ceiling would be absorbed in the middle insulation and probably foster mold and extensive water staining of your new ceiling. This situation would be impossible to fix without tearing out sections of your new ceiling.

This is the way we usually install a new drywall coat:

Secure any loose areas of plaster with screws or remove them.

Determine the lowest point of the ceiling. This will be the reference point for the rest of the ceiling. I use a laser and a tape measure to find the low spot and mark a reference line on the walls 2 inches below that point. You could rent a laser or buy a basic 360 degree model for around $70. The old fashion way is to use a water level or run very taught level strings.

Using 2 1/2" X 3/4" strapping, run them perpendicular to the ceiling joists at 16" on center. Shim these using tapered shingles or small wood shims to the 2" reference. (Again using your laser and tape measure) Nail these into the joists. I use 2 1/2 inch threaded nails in my framing nailer. Fill in around the parameter of the room with strapping. This procedure will give you a nice flat, secure and level grid to install your new drywall on.

Don't forget to install extension boxes for any electrical fixtures.