I will also agree do not worry so much about getting heat up, worry about getting cold air down and then no fans are needed
, yours stairs will work well for hot air feed but you need something to replace the hot air going up.
Cut your cold air returns in, and run a pipe at least 18" down from the ceiling, personally I would go to within a foot of the ground. This way it assures only cold air comes down and no hot air trys to mess up your return.
Also why is your stove 600* already, if that is the case you are going to need a bigger stove