I looked at this article - a lot to think about
:
http://www.fishnick.com/ventilation/designguides/CKV_Design_Guide_2_031504.pdf
I started wondering where/how 700 cfm can exit a 14" duct (1 sq ft) at 12 ft/sec, that is close enough to the range to satisfy the goal (2) without disrupting the airflow required for the hood to capture all smoke/grease per goal (1). I think you're right, goal (4) isn't going to happen.
I was originally thinking a duct under the floor (full basement) to a floor vent under the range, which would be a space about 6" tall. If the range is free-standing (no cabinetry on either side) then the air will have about 4 sq ft to come out (front and sides), so should slow to 3 ft/sec. Will it then turn upward and flow smoothly up the sides and front of the range, past the cooking surface, and up into the vent hood - sort of an air curtain idea? Or will it simply make the floor really cold, unless deliberately directed upwards?
The "backwall" design shown in the article seems interesting, though I'm not sure why the duct seems to point down not up.