Actually, after posting that and starting a thread specific to my problem, I continued reading among the dozens of similar threads about this sort of problem -- and surprisingly enough I found one post in one thread that actually had a useful answer.
It turns out that WLM stores the Outbox emails as individual eml files in a folder
C:\Users\username\AppData\Local\Microsoft\Windows Live Mail\Outbox
with WLM not running, you can navigate to that folder and simply delete the eml files.
Windows will complain that you need Administrator permission even if you are using an Administrator level account, but you can tell it to continue and it will let you delete the files.
This will let WLM open properly -- depending on just how screwed up WLM itself was, it may still think there ought to be one or more files in the outbox, but after the eml files have been deleted it is then easy to follow the conventional advice of going to the Outbox in WLM to delete the emails (which at this point, it can't find but will let you delete anyway)