This isn't that strange -- you are looking for 6 D1 tickets on a direct route and you need them at the saver level if you booked via VS (e.g., even if DL did show availability but with a crazy high miles price tag, you wouldn't be able to book them with VS miles). It's virtually impossible that you will ever find that on the same day and same flight, especially at the saver level required for VS to book a partner award. Plus in theory the Olympics are happening later this year so there's no reason for DL to make any award seats available on those flights in case they can be purchased by people traveling with the Olympic teams and their associated parties.

You are going to have to be flexible (book with a connection, split the tickets into groups of 2 or 3) if you want to keep these seats into the future.