Is there anyone out there who thinks the prop should be turning? I ask
only because the people who have been doing the flushing for years do
have it turning, and I know they are going to argue with me.

I likewise flush my 6hp dinghy outboard using a trashcan and a wood block
jig mounted on a handcart. If the water exits via the usual 'pee' stream
then it wouldn't seem to matter. I've run mine both in and out of gear and
the stream was unchanged. It would seem unlikely it'd make much difference.
That and unless you're cranking it full throttle I can't see it doing much
to starve the intake of water.