My apologies for posting this here. It really should have been posted to StackExchange, but I do thank you Torsten Link for your comment. It got me halfway there. And in case I've piqued anyone's interest, I'll go ahead and post my solution.
The first thing I had to realize is that Folders and Views are two different things.
- A view will list documents based on a pre-defined search criteria.
- A folder contains documents that have been marked as being in that
So while I could use
NotesDocument.PutInFolder(FolderName) to get a copy of the note into the specified folder, it didn't "remove" it from the sent view.
To remove it from the Sent view, I had to cause it to fail the Sent view's search criteria. In this case here is the code for the sent view.
SELECT DeliveredDate = "" & PostedDate != "" & !(@IsMember("S"; ExcludeFromView))
This means the following.
Show the document in the view if the field "DeliveredDate" is blank and PostedDate is not blank, and the field ExcludeFromView does not contain an "S".
So, to keep the item from showing up in the Sent mail view, I had to add an "S" to the existing value in the ExcludeFromView field.