Hi and Welcome!
I was lucky in that the end of the cold air return duct was right over the stove. There is a
6" hole cut in the top plate and a steel bar under the plate,
to the front side of the hole, to stop the convection
air from coming out the front of the stove. then standard 6" pipe connectors up into the
cold air return. I run the stove fan, and also the furnace fan. the air in the system is not
all that hot, (depending on how hot the stove is) but it does keep the house a very constant
temp. I have the homes cold air returns on the first floor just about closed off, not fully, but
wanted to force the furnace to pull more hot air into the system. Another little helper for it
was i found that there was a "patched" hole in the cold air return very close to the end of it's
duct, on the bottom side, which is in that same vicinity of the stove, so i removed it's patch and
that allows the cold air return to draws more air from the ceiling area above the stove as well.
my thoughts were to get as much
warm air into the system as possible, and try to take as much heat out of the basement as possible
and push it upstairs. As of now, we are not heating the 2nd floor of the cape cod, so those heat
and cold air runs are closed off.
I can't say how well you will do trying to take air downward into the cold air return. It might be worth
investigating where the nearest cold air return for a 2nd floor room might be, and if there is one
next to the stove tapping into that pipe thru the wall might be an option. i'm not sure how your home is laid out.
as far as your idea, i would think you would be better coming off the top of the stove, maybe go with
larger square ductwork off to the side and down into the cold return thru the floor,, i think it'd be pretty
ugly to have in your living room though! being in the basement we really don't care too much about looks,
and everything i did was more of a test run, and from what we saw this winter it's going to be the way to
go in the future for us. just started into my 4th ton of coal.