Any chance the columns  were set to Hidden in the list's content type
management interface?

No- we actually aren't using content types in this library.

I remember having problems w/ moving docs in content and structure in the past,
because it would copy over the other libraries properties  (even if they were
named/designed exactly the same), and weird stuff like this started happening.
But as soon as I deleted the "carried over" columns, everything seemed fine.
I tried that w/ this, but no luck. The problem was evident before and after I
deleted the carried over columns.

I wonder if, since in datasheet I can still see all of the old properties, if I
should just create new columns  w/ similar names, use datasheet to do a mass
copy/paste of the stuff, and then delete the old (corrupt?) columns. Not too
keen on my name showing  as the last modified person, but it may come to that.

I unfortunately still have no idea  what happened  and why the properties  went
missing, but I decided to do the following to "fix" the problem at hand:

1. From a view of all documents and important columns  (including modified by and
modified), I exported to spreadsheet and saved it so there was a "snapshot in
time" of the properties that could be used in the future if necessary.

2. Turned off forced checkout

3. Created new columns for the properties and just added a "1" to the end of the
name

4. Removed the requirements from the old columns

5. In datasheet view w/ old columns side-by-side w/ new columns (three old then
immediately three new in the same order), I filtered out all "checked out"
documents (only 11), the copied and pasted the data from the old columns to the
new. I ran through all 800+ lines just to be sure everything copied properly.

6. I modified all old views (including web part views) to use the new columns in
place of the old

7. Deleted (gasp!) old columns

8. Reset column requirements and forced checkout

It appears the only MAJOR downside to this "solution" is that we've lost the
modified by and modified date history since it now shows me and today's
date/time. That's why I exported to spreadsheet first, JUST in case they need to
use those columns to find particular documents. I also (of course) confirmed w/
the team that it was okay w/ them to lose that particular system-created
metadata.

Whew! I'm praying this fire has been thoroughly extinguished. I had the site
admin for that site double-check everything, and she's happy. I think we're good
to go!

Hope this helps someone in the future. And just BE VERY CAREFUL when using
content and structure to move docs from one site's library  to another. I still
don't understand what exactly is happening "in the background" but it's
definitely some bizarre behavior. I think this particular drama was more severe
than other experiences I've had w/ content and structure, but none of them have
been very fun to identify and fix...