Hi,
I'd like to add another addition to your rules, in that double-bills can also be films that are linked, but not necessarily in a blatantly obvious way. As long as whoever suggests the double-bill explains what the "link" or "theme" is, then that should be allowed too.
They're are plenty of double-bills you could do, that don't necessarily seem obvious as to their links. Examples, could include:
KIKI'S DELIVERY SERVICE and THE CAT RETURNS (both feature cats as main characters, as well as being Studio Ghibli films)
RIPLEY'S GAME and PLEIN SOLEIL (both are based on Patricia Highsmith novels, but hardly anyone remembers either of the films. Everyone only seems to remember THE TALENTED MR RIPLEY!)
RUNAWAY TRAIN and AMATEUR (and/or THE EEL) (All are Existential action films)
DAS EXPERIMENT and THE BAADER-MEINHOF COMPLEX (Two excellent and rarely-seen German dramas based on true-life events)
FEMALE TROUBLE and SILENT NIGHT, DEADLY NIGHT (and/or CHRISTMAS EVIL) (An anti-Christmas double-bill!)
THE GIRL NEXT DOOR and THE GIRL NEXT DOOR (Same title, two very,
very different films!)
Etc, etc.

I'm not here to include myself in the double-bill club, merely offering some interesting and provocative double-bills that some of you might want to consider. My thinking tends to be very much outside-of-the-box.
Pooch