The biggest problem I see is that most of your sizes do not have a common denominator and a few that are primes (the 13 and 17) so not evenly divisible by anything. The only option you have is to use filler strips like osewme suggested. I would lay them out on a design wall or bed in the placement you (or your son) wants and start measuring for your filler strips. Don't forget the seam allowance. I did that when I made this quilt: https://www.quiltingboard.com/pictures-f5/double-sided-t-shirt-quilt-t209647.html but even on this one most of my shirts were cut to sizes that were evenly divisible by 3 so I had (in finished sizes) 3 x 3, 6 x 12, 12 x 12, 12 x 15, etc. so I was able to sew the quilt together in quadrants. The devil fishing shirt was the one odd size and I used filler strips. The shadow box layout helped too.