This issue has now been solved. The problem was being caused by the DatabaseName property of the MS SQL Server db not being specified before making a connection, such that after a query was made and stored in a RowSet variable, the application would hang, massively slowing down the time to write the data from the RowSet to the in-memory SQLite database.
After specifying the DatabaseName property of the database, the time to write to the SQLite db reduced from around 170 second to 0.6 seconds!
Here is the post where I identified the issue when I focussed on just retrieving the data from the database (and not writing to the SQLite database).
I suspect this is a bug and so I will raise the issue.