Ultimately, it is up to you how to move forward.
Most would recommend tearing up the 1/2" and putting down proper 3/4".
I'm sure you could find a way to support the 4" overhang if you have access from below.
If you elect not to tear up, gluing down another layer of 1/2" is an alternative. I'd recommend the pricier Titebond-III (TB-II is also excellent and while it will be cheaper, it does have slightly less open time and is not waterproof), roll it on with a low nap roller (paint it on) or the flat side of a trowel or a wide taping/drywall knife. I'd further recommend coating both sheets of ply with the glue and then use these
Grip-Rite coated deck screws with the star drive at 1 1/4". You won't need a pilot hole and they are threaded 2/3s of the shank to help mitigate screw jacking. You'll pay more for these but they drive like a dream. Get a partner to help with all this and it'll go much smoother. You'll have to move it when laying out the glue to get the sheets married before the glue skins over.
Once you have that completed, it is up to you as to your choice of tile underlayment: Hardibacker, Ditra, Greenskin, etc.