I just made a post about this a couple of weeks ago... so search my history to find it. Even though it was on a Canon, I'm not surprised to see Epson's have this same issue. It really isn't the canvas shrinking in my opinion, its that the printer cannot accurately tell how much it is feeding the canvas. Some people play with the feed adjustment in the printer, and although I'm not familiar with Epsons anymore, I think I remember people saying they use values such as +10 or so, but I have no idea the units or anything like this. Since you know it came up 3/16" short, you could just stretch your image, without changing the size in the other dimension by this same 3/16th. So essentially, instead of printing an image that is 16x20, you will print an image that is 16 x 20.2 inches, or something like this, which is what you're thinking as well.
For canvas, having a bit extra is usually ok since it can be stretched around the size, but since you're framing, I guess you want it a bit more precise. Knowing that you're off only 3/16 and want to print just this size, it should be pretty easy to get it close enough and if its just 2 mm's or so longer, I think this would be ok ,and certainly better than it being too short.