I'm a huge fan of the 136DD. You can have the frame layout of most 14' boats in a 13'6" package and the diminishing tubes up the fun factor as well. I've had a handful of the 136DD's through the shop in the past year. They've all been on the skinny side of the spectrum. I put 36" wide boxes in them as the interior width was like 36.5"-37" most of the time. A 38" box required more force than I was happy with, especially when I could do 36" boxes and not have any issues. I'm sure a 38" wide would be fine, just depends on what you get. I've noticed they all seem to vary 1"+ from time to time. If you're concerned, I'd wait till you physically have the boat in front of you and measure it. It might be close to 38" in the middle but at the end of the straight section I have yet to see one that wide where your dry boxes will go. I'm sure they are every bit of 38" or more with thwarts installed.
I 100% agree on the Prospector cooler. 95% of all my boats go out the door with that cooler, and it's a perfect fit on the 136DD.