As you say you want to use screws and it's non-structural, I'd go with:

Get some 4" wood screws, drill half way down through the upper piece with a drill slightly bigger than the screw heads, you shouldn't need to do pilot holes all the way through as 2" really shouldn't split unless you use huge screws.

I'd go with 4 or 5 screws along the length.

Screw down through the top piece until you get a little bit of the tip poking out (say 1mm)

Align the top piece on the bottom piece, give it a knock to set the exposed tips into the lower piece, and screw down.

If you don't want exposed holes do it the other way up, if the lower piece is not already set in place.

Without using dowels, how do I join 2x4s edge to edge to be 1.5" x 7"?
When you give the player a rare but powerful item which can only be used once but is never really required to proceed, most players will not use it at all, because they are waiting for the perfect moment. But even when this moment comes, they will still be reluctant to use it, because there might be an even better moment later. So they keep hoarding it for a moment which will never come. 

In the end, they will carry the item around until it is outclassed by other, more readily available resources, or even until the very end of the game. That means that such one-shot items don't provide any gameplay-value at all. They are simply too awesome to use.

What can you do to encourage the player to make use of their one-shot items and not hoard them?
