I like Paul's method. But one thing to keep in mind is your 2x4 is probably not dry and may move even more. If it does that after you attach your patterns you would have a big problem. Framing lumber is far from dry and will move all over t he place till it stabilizes. And that can take months.

I assume your not a woodworker. But if you are or know someone who is. I think a plywood box beam would be better. Cut 4 strips and dado edges and screw them together into a hollow box, that should make a really strong and straight beam.

As someone else suggested my second choice would be laminating several strips together. That would be heavier but it would be strong.