Dayton wheels, made in the last 15 years or so, have the inside edge of the outer splined hub machined true to the wheel center. This means that balancer cones can be used on both inner & outer sides of the wheel hub.
I believe that older Dayton wheels may not have had this "inner outboard cone" mating surface machined true. I'm pretty sure that none of the Dunlop wheels have this surface machined.
Wheels that do not have this true machined surface will require a funnel rather than a cone on the outside of the hub to hold the hub the same way as the knockoff spinner does. Thus the "spline" part that Moss refers to.
You should be able to check which wheels you have. If there is a taper on both the inside & outside of the outboard hub shoulder, and the shoulder's thickness measures the same within a couple of thousandths at different points around the hub, (concentric inner & outer surfaces) it will work with a balancer cone on the outer side of the wheel.
I'm not sure how reversing the wheel would solve the problem of no machined true surface on the outboard inner hub shoulder. But maybe, somehow?
Have you considered that out of balance is sometimes caused by non concentric machining of the brake drums. The drums can also be balanced & often helps greatly.
D