The outboard floor vents are connected to the wing root openings.

The heater vents run along the center tunnel between the seats.

The overhead vents connect to the vertical stabilizer opening with the
blower in between.

Yep, but he's not talking about ANY of those vents.

There is a fine grating piece that fits alongside the rear seats,
between the seat and the outer wall of this model of Cherokee. This
grating allows air to flow freely the cabin and the under-seat
compartment (where the battery is on some Cherokees), and then out a
hole in the bottom of the plane.

Think "flow-through ventilation", circa Pontiac 1968.

That hole has a shroud around it that makes it act like a venturi in
flight, actually SUCKING the air through those mesh grates, and out the
bottom of the plane. For some reason, the OP is getting air coming OUT
of that grating -- only on the right side -- which is seemingly
impossible.
--
Jay Honeck
Iowa City, IA
Pathfinder N56993
www.AlexisParkInn.com
"Your Aviation Destination"