Huck you can barely see it, but on the board #003 I made, I added a half bonzer bottom. By half bonzer, I just started the concave further back then normal bonzers, about a fourth of the way up from the tail. If you have small holes on the bottom, you could add concaves.
If it’s soft on the deck along the stringer, you may want to add a piece of veneer. That’s one problem with PU blanks. It will start to cave in along the stringer then the glass will crack and water will get. A veneer strip over the stringer about 6" to 8" should help stop that from happening.
Looking at your photo again, I realize it’s at an angle, so it’s hard to get a true idea about the outline. At the width you’re talking about, it may be OK. if anything just make sure you thin the rails down enough to bury them when you turn. If you make the tail like the 2 boards the other guys posted, it would be OK as a single fin. I use a 9" single fin. I think there are 4 different fins on my boards. Jr Boy, L flex, cutaway and Greenough stage 4a.