Do you have to rip up the top layer? Is it trashed, squeaking, wrong elevation? If you're screwing it, why not go through both layers, tighten the whole thing up, save some demo work and have a stiffer floor overall? Obviously I'm not there and don't know what the current state of things are.
IF you only have 1/2" left, most hardwoods require a minimum of a 5/8" subfloor under them, that's why I say that. It ALL DEPENDS ON WHAT YOU'RE PUTTING DOWN. Hopefully you've already got it in the house, it really should acclimate for a couple weeks, especially being spring time and having the humidity and temperature changes so drastic right now. If you're unsure up the plywood thickness that you're left with just take a drill and pop a hole in it somewhere and measure it.
Are you going to run perpendicular to the joists, or try to run parallel to them? Are they 16 on center? (Edit: just read that above)
Screwing every 6" is perfect for tightening up the whole floor if it needs it. What do you plan on for an underlayment? Are you over a damp basement or dry living space. I would go 15# felt if there's any chance of dampness coming up from below, if not red rosin paper should be fine.
I just throw the above out there because, being in the trades, more than once, I've see a floor look great when it goes down (without proper prep) and then in two years you can see where every floor joist is. Know what you intend to put down, look at what they require for a sub floor, follow instructions, will last a long time.
Here's a couple we did in the past month. One was 900 sf. the other is about 700sf (in process).
Good luck.