With respect to the wood route, are you talking about laying the parkland onto the wood, or the border to the wood?
If the former, people are using the parkland recommended adhesive, laying the sheet onto the wood, and then using a laminate roller to flatten the screen to the wood.
If the border is what you were asking about, I was going to attach the border on top of the screen and then glue/screw the border to the frame. Depending on the thickness of your backing material and the border, you could even router out a section of the backing so that the border wraps around the edges of the backing.....much like a picture frame is designed to hold the glass.
As to the border routing...you got it! Rather than havinga square edge for the screen side of the border, you could route it at an angle so as to avoid any shadows cast onto the screen (might be more prevalent with the square edge). I know that Dalite does this with their more expensive screen frames - aluminum.
Cheers,
Simon