Thanks Paul. Left you a voicemail

Replying here for the benefit of anyone following -- the trick to
getting a region defined, I discovered, is to hold down the Ctrl key
while using the left mouse to click and drag a rectangle on the map
display (which must be brought up using the red "AS" button). Right-
clicking on the map and selecting "Regions" brings up a dialog in
which you can give the newly defined region a name and add it to the
internal region list.

After loading the exported .CUB files in SeeYou, I further discovered
that the Tim Newport-Peace (.sua) file format is not a friendly source
for LXasBrowser -- almost all of the controlled airspace regions came
up with incorrect class names! ("Class A" for the Tucson Class C,
e.g.) (Tim, Crtomir, any clues?)

Using the OpenAir(TM) (.txt) format worked fine, however.

The procedure I was looking for in my OP goes like this:
1) Run LXasBrowser.exe and click File | New Workspace.
2) Click File | Open and load your source file (for me, that's one of
the OpenAir files from justsoar.com).
3) Click on the "New Data" button in the toolbar below the main menu.
4) Click on the red "AS" button to view the airspace and set or create
the region to use (as described above).
5) In the main LXasBrowser window, click on Transform | To CUB. In the
Airspace Info dialog that comes up, specify the name that will be
shown in the LX instrument and click Ok.
6) Specify a disk file name (.CUB) and click Save. You're done (except
for getting it into the instrument without letting any of the smoke
out, of course).

~ted/2NO