The Tremec manual, and both by Motorcraft and Alldata online manual that I have subscriptions to all say 3.1 litres (3.28 US quarts). Online service manual are continually sync'ed to show the most current data and specifications.
Sometimes the owner's manuals are correct, sometimes they aren't. Ford, NHTSA, and Tremec are always performing ongoing R&D on their producs. It was found that the TR3650 actually worked better with about a 1/4 quart less fluid.
Lucas Semi Synthetic ATF, Redline D4-ATF Synthetic, and Royal Purple Synchromax are all great products. I happen to like the Royal Purple products in particular. The Synchromax is specifically designed for manual transmissions that call for ATF. The GM Sychromesh is also a good product for the 3650's.
The TR-3650 uses a hybrid organic/carbon fiber friction lining on the friction face of the blocker rings. The Royal Purple Sychromax and the GM Synchromesh are specifically designed to have a low sulfur content and work best with those specific type of blocker rings making gear engagements as smooth as possible.