making a rabbet in plywood
You wanted to drill away the waste with a Forstner...right?
Why not just make the rabbet by using smaller size pieces and offset them to create a rabbet... no drilling required?
How will you cut the pieces, by hand saw?
How will you get them accurate?
Joinery requires accurate mating surfaces for strength and gluing area. ...gaps won't work well.
What are you making that requires a 2" thick piece?
If you want to secure the pieces until the glue sets up, I would use brad nails which will not split out the layers of the plywood, not screws. Clamps would be great, but it doesn't sound like you are equipped for that. Band clamps can be made with ratchet straps, bicycle inner tunes or by wedging against a block on the bench.
The answer to your question will only be as detailed and specific as the question is detailed and specific. Good questions also include a sketch or a photo that illustrates your issue. (:< D)