Couple of thoughts ... (1) Before adding wood, check the downstairs ceiling for any sagging. If there is a sag, use screw jacks (with a 2x6) to push up the sagging joist before adding wood or re-attaching upstairs. (2) I would use PL Premium construction adhesive applied in a "sine curve" pattern to sister new 2x6 lumber. It will hold really well. Highly recommended. (3) You can block around the vent but try to install hanger metal to beef up the strength of the connections between the joists side-to-side. Now, if you sister new 2x6 joist wood, use a double joist hanger for the new connection. While you are there, with the subflooring removed, you can retrofit joist hangers to the joists which you can reach. (4) if you really want to lock it all in, apply the PL Premium on the top edge of the new joist framework so you can screw down the new sub-floor.
YEAH! That's what I'm talking about . . .