Here's what I came up with to get my measurement. I put all four pieces of the frame together like I did before. But this time I placed some parallels inside the groove, then I removed one side and took my measurement.
 

Very carefully, I placed one end of my scale against the left side parallel (out of view). Then I took my measurement by looking carefully at the business end. And as you can see it's about 15.250". With this number in mind, I'll cut my plastic slightly smaller than this so it will fit without any binding.
 

I bought a piece of acrylic from the hardware store but had them cut it larger than I needed. Then I used my bandsaw to rough cut it 1/8" oversize of my final dimension.
 

I wasn't able to place a clamp in the middle while milling so I slid a piece of thin cardboard under the board (in the middle) that was clamped on top. This made the top piece 'bow' slightly which put pressure against my plastic acting like a third clamp. This worked great and I was able to machine my work piece without any problems.
 

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Here I'm doing some test fitting with the help of some 1/8" thick parallels under my plastic. These parallels raised the plastic high enough so I could slide my frame together, which acted like a third hand for me. And the plastic fit perfect so my calculated dimensions from earlier worked out pretty good.
 

Now it's time to put in some screws to hold the back on. I'm going to use three screws on the long sides and two screws on the short sides. Below I'm drilling some clearance holes for some #4 flathead screws.