Plywood underlayment over plywood subfloor - how to secure
First, I'd counter your plans to orient the second layer perpendicular to the subfloor. Plywood and OSB have a strength axis that should run across the joists. Instead of turning the top layer, simply stagger its joints with respect to those of the subfloor. Start with a ripped half sheet and stagger the butt joint by two joists. 

I've never heard the advice you mention about avoiding joists with underlayment fasteners. It's probably not critical to run screws into joists, but there are a couple reasons why you would. 


Running through between the joists creates some possibility that you'll hit something underneath that shouldn't have holes in it. Using 1-3/4" screws it's not likely to be a problem, but it is possible. 
You may find your screws stripping at the threads before the heads are completely sunk. They should be at or below flush, and that takes quite a bit of pull from the threads. 


I wouldn't worry about gapping butt joints with plywood. It's stable enough that it shouldn't be a problem unless you happen to be installing very dry wood in a very humid environment. OSB is usually undersized to allow for swelling, but not plywood.