Two inches is what you would want, yes. There won’t be a lot of strain on it if you clamp on the plywood itself. A “C” clamp on each side and a stick across the lamination is the way to go. There will be a tendency for the pieces to cup on you so the more clamps the better. This may be a place for some all thread, some wingnuts, and some creative thinking.
The early bird gets the worm but its the second mouse that gets the cheese.