Hi, I would rely mostly on construction adhesive. You are looking to mostly avoid subtle movements that might cause squeaks or bumps in the night. You don't have to worry about the floor flying away, so in addition to the adhesive you probably want to power nail a couple blocks of 2x4 on the flat (with a little glue too) right next to each joist about a third of the way out from each end. You can then put a couple screws through the joist, into the blocks. This will give you the mechanical bond you are looking for.
Things to remember:
The floor will probably end up being a little higher than you plan. Be conservative, if you try to end up 1/4" lower than your existing floor then you will probably end up flush. If not, no big deal, you will have a 1/4" drop or you can add 1/4" luan to be perfect. I have seen up to 1/2" higher tile next to wood floors not be a tripper. Shoot for perfect and settle with close enough. If you shoot for close enough, you usually end up with close, but no cigar.