Can I 'glue and screw' 1/2" and 3/8" plywood sheets to substitute for 7/8"?
I wouldn’t try to laminate two pieces of plywood together. 

Group 1 type plywood is rated for various spans. Using 1/2” plywood to span 16” will span the distance without failing, but will have too much defection. That is to say, it will be springy. It’s designed for 2 span installations. If it’s a one span situation, it will be noticeable. 

Adding additional plywood layers does very little to decrease the deflection problem and if the adhesive is not installed correctly (and cured correctly) it could create other problems, like 1) bulging, 2) warping, 3) delaminating, etc.

I’d use 3/4” plywood with the wood strips you suggest. 3/4” plywood will be stiff enough that you could use in a single span situation and still be acceptable for ceramic tile floor, etc.

Also, remember to install with the face grain perpendicular to the joists. (Screw and glue...adhesive... to insure no squeaks.)

Also, this is for “subfloor” only. You still need an underlayment. Check with the manufacturer of your finish floor material to see what they require for an underlayment. (It’s different for ceramic tile, vinyl, etc.)