RESOLVED
Here's what worked for me. I did two
things. I'm not totally sure which one did the trick, but I
successfully added a SQLite connection to solution in VS 2008.
(1)
I went to the properties of the solution (Tools >> Options and in
Options "Database Tools" >> Database Connections. I set the "SQL
Server Instance Name" to SQLite Database File
(2) In the Machine.Config file in the Windows Directory, I commented out the default DB Connection type (which was SQLExpress).
After I did those two things, I did a full reboot.
After
the reboot, when I opened Visual Studio and attempted to add a new
connection, I got a much more elaborate dialogue box which included the
'picker' to pick a SQLite Database. Since had also uploaded the SQLite
Northinwind Traders, I pointed to that and clicked "OK".
The
installation of the connection completed. I was dancing and singing.
I still haven't used it or queried the DB but I'm one step further
along.
Good times. Hope this helps.