Thanks for the thoughts, guys. Stephen - that is one good-looking underside. Gives me something to aspire to. Did you use POR-15 and then the color coat?
The underside of my car was indeed typical of a very well-preserved 39-year-old car when it went in to the body shop. I have owned it since 1985 - bought it from a dealer when the original owner traded it in on something. The car came from NC, so it has always lived in the South. It has had almost no rust anywhere. As far as I am aware, this is the original 1974 undercoating that is coming off. (And yes, that is a great paint job on top - Dwight Burnett, Quality First, Brandon, MS.)
When it went in for paint in September, I couldn't afford to do a complete take-out-all-the-systems restoration, and the bottom (and engine, etc.) looked good enough to everybody so that I elected to have a good paint job on top and then to drive the car as I gradually worked on the systems underneath. (e.g., I'm replacing the brake system right now.)
I agree that the stalagmites look like rubber-based paint, but it all looked like regular undercoating a year ago. I certainly haven't put any paint-like substance on the bottom of the car in the 24 years I have had it. The soft, floppy stalagmites are mainly in the center of the car, whereas around the edges the undercoating is flaking off in a drier form. Could blown-back drips of the synthetic oil I put in six monthe ago be affecting the undercoating? Seems unlikely. (Nevertheless, I plan to change back to dinosaur oil today - oil drips under the car have increased markedly in recent months.)
The metal underneath the falling undercoat all looks shiny brand new just-off-the-assembly-line. (A complication for the POR-15 approach.)
Anyway, I really appreciate all your comments.
Here is one more view: