Some more diverse testing reveals that the problem seems to occur only when SSMSEE is running on Windows 2000.
The source of the problem appears to be that W2K is not picking up the correct instance name (in other words, it puts MYSERVER in the list of engines, but not MYSERVER\SQLEXPRESS). If I key in MYSERVER\SQLEXPRESS by hand, things work as expected.
Incidentally, I noticed that when running under XP, the Network Server list shows which version of the SQL Engine is running on each server, but under Windows 2000, it does this only for very few of the servers.
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