How best to join 2 layers of sub floor?

I have had to raise the subfloor in multiple rooms of my house to bring everything up and level with my kitchen floor. The worst discrepancy is the 1" between the kitchen and den. To level off I will be raising the den floor with 2 layers of 1/2" fir plywood. How should I best fasten these layers of plywood to the old plywood subfloor?

My current plan is to apply lepage PL400 in lines 12" apart and on the edges, use 2 1/2" flooring screws and screw into the joists (12" apart), fill seams with floor patch on each layer, and criss-cross the plywood so that no seams align.

I have read elsewhere that the fasteners for additional layers of the plywood subfloor should not penetrate into the joists, but I could not find a reason why this shouldn’t happen. Is my method here out of line? Wouldn’t affixing the plywood layers to the joists reduce squeaks?

Thanks