Heading off an area is usually for openings carrying no load, like skylights, stairway opening etc...You have a floor load above these joists so you cannot simply header off these joists, what would carry the above load ?
If you move the duct work up into the headed off joist area your going to have a 90 degree bend getting up into it, a 90 degree bend transitioning to inside the floor joist area and the same again on the way out of the new area, that's 4 x 90 degree bends, you might find yourself in some serious heating and cooling deficiencies, have you spoken to your HVAC guy yet ?
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