How to Lay Luan Plywood Over the Sub-Floor
If the subfloor is in good shape then there is really no need in installing luan plywood on top. Just regular straight edge plywood will do and then it will be a little easier on you with less waste.
For the strongest floor, you want the sheets running in the same direction as the subfloor, which is perpendicular to the joists.
With thelong edges of the luan sheets should be offset from the subfloor by at least 4", and more is okay. The short edges of luan board (plywood) should 1/4 of the way between the joists, for example 4" from the joist if they're 16" O.C. and 6" if they're 24" O.C. You are correct about the spacing of the sheets.
Also make sure to screw the two layers together, but avoid hitting the joists. The easiest way to do this is to use screws that are the same length as the thickness of both layers, 1 1/4" in your case.
Sometimes it's not possible to find screws that exact length, but you can find 1 1/2", and that's okay since you'll have very minimal penetration of the joists with that size screw.
You want screws every 4-6" around the perimeter of the sheet, and every 6-8" in the field. Use deck screws, not drywall screws. You want them seated flush, but not below the surface. Depending on how many square feet you have to do, you may want to try to get your hands on a deck screw gun.
If you go through 50-60 screws per sheet and have 30-40 sheets to do, it can be very time-consuming and back-breaking.
This will give you an exceptionally strong subfloor that should hold up to just about anything.