How much weight would a 3/4 Volan deck patch add? I'm thinking that could be the happy medium.
If you want to get a stronger board then start with epoxy. After that you can dial the weight in to suit what you're trying to do.
One time I had a board that I built that was too light for what I was trying to do so I went back afterwards and added another layer of 4oz to get the weight right. It turned out just the way I wanted it.
As I said before, with a fish some glide can be a good thing if you intend to surf it that way, or you might opt for lighter if you don't want the glide.
Your shaper is stearing you in the right direction - Do double 4s top and bottom. For flex - for a board that short, its basically non existent. Especially at your weight.