A few issues: a san-tee can't be used on its back/side like that for drainage, you would need a combo. But the vent takeoff can't be horizontal. And the AAV has to be accessible, e.g. in a wall box with a ventilated cover.
So basically you need to route the tub drain under a wall (or almost under a wall), so your vent takeoff can be vertical (or at least 45 degrees above horizontal). I believe Ohio follows the IPC, so your 1-1/2" trap arm could be up to 6' long (distance from trap to vent). Or you could use a 2" trap with a trap arm up to 8' long. In both cases the total trap arm fall can't exceed the pipe diameter, so to achieve those lengths you need perfect 1/4" per foot fall on the trap arm.
Seems like you have two options: change the elbow at the top of your first picture to a san-tee, if you can get a vent pipe from there into the wall without going horizontal (staying at least 45 degrees above level) and without hitting the tub.
Or you can point your u-bend outlet towards the wall right there with the water supplies, point your p-trap elbow outlet parallel to the wall, use a san-tee on its back (allowable under the IPC) for the vent take off, rolled 45 degrees off vertical, with the vent hitting a 45 under the wall to turn vertical, and then a long turn 90 to turn back towards the existing galvanized drain. Getting that all to fit in the joist bay may be challenging and may require the use of some street fittings. Plus you might need to move the water supplies out of your way.
Probably the second option is simplest/best if it will fit, and if you have a place in that wall for the accessible AAV vent box, or if you can run a dry vent up into the framing above (or attic) to connect with another dry vent.