I hope this makes clear the general sequence of events that led me into this 
mess. As I pointed out earlier, if these browsers work fine in XFCE but not 
in TDE, then it seems to me that this ought to concern us who run TDE, as it 
could be a sign of what's to come. 

Did you install TDE using the tde-trinity metapackage, or some other way?  I think, in your position, I would purge TDE, reinstall using the metapackage, and see what happens.  If that doesn't work, next thing I would try is some other distro, like MX Linux.

-- 
PGP key: http://homestead-products.com/pubkey.htm