Well, I have gotten no answers since I posted this questions. But I have figured some things out on my own.

• There is not a way to save off the screen and later restore it.
• When programs seem to be doing this (e.g. vim, htop etc), what they are actually doing is switching to an alternative buffer. When done, they return to the primary buffer. And doing this effects restoring the prior contents of the screen.

I found discussion of this here.

The syntax is ESC[?1049h, and ESC[?1049l -- here 'h' activates the alternate buffer and 'l' returns to normal mode. Other similar codes are 1047 and 1048. But apparently they are older and have less functionality.

The fact that this code starts with ESC[? apparently indicates that this is a private setmode, and functionality may vary across various terminals.