If your x-seam is 44.5 inches, add 3 1/8 inch to this to get 47.625 inches. The crank should be 47.625 inches ahead of the place where the seat bottom meets the seat back. At least, that's the way my wooden homebuilt LWB recumbent bike is. My seat back support post makes an angle of 57 degrees relative to horizontal. A straight board goes from my rear wheel support to the bottom of my seat to my crank. This board is tilted upward at 7 degrees from horizontal, so the front end is slightly higher than the rear end.

Your bike's geometry might be different. I recommend that you get big cardboard boxes to cut out templates. You know, refrigerator-sized boxes. Then you can experiment with cut-out cardboard pieces to make sure the geometry is right for you before you start cutting bamboo. All you need is big pieces of cardboard, a razor-knife, and a Sharpie.