Hi @eric_engineer,
When you make multi-gated parts in the library you can name the gates something more sensible. The most common option is to use letters for the gates A, B, C... also in the device editor click on the Prefix button and define the prefix you want the component to have, the U$ default isn't useful generally.
In regards to the Invoke functionality you are correct but select and drag should work. You have to drag to the edge of the drawing area move into the sheets section, select the sheet you want and then when you hover back over the drawing area you'll see the part floating on your mouse cursor. Agree this workflow could be better.
Best Regards,

Jorge Garcia
Product Support Specialist for Fusion 360 and EAGLE
Kudos are much appreciated if the information I have shared is helpful to you and/or others.
Did this resolve your issue? Please accept it "As a Solution" so others may benefit from it.