Chris
Just put a 1/8" thick lam between the backing and the core that extends to the end of the handle or just past
Exactly, a power lam. But, just to specify, it needs to taper out to nothing out past the handle.
Doesn't take much.
The thing with dowels doesn't work a lot better than just gluing on the handle lams, IME. I have had success with it on lighter weight bows, low 40's max, by angling the dowels through so they come out on the handle closer together than on the front. It's not the best way, though. A real fadeout, created by the power lam,or by starting with a belly lam at least 1/8" thicker than needed works.
Lastly, some are saying the thickness you have total there is not enough, but if you put reflex, recurves, or R/D in it, esp with Perry reflex, it will be. I glue up most of my laminated bows with a 3/8" belly of something really good, and an 1/8" inch backing.