I can’t quite figure out if you are filleting the edges of the solid or the original curves. If it’s the first, you can simply use FilletEdge and window-drag across your object to select every single edge in the object. if you have very small edges, pay attention to the fact, that your radius can’t be smaller than thsoe edges. Rhino’s FilletEdge can’t eliminate faces.
If it’s the latter, you can use FilletCorners to fillet all corners of a polycurve/-line in one go.
I don’t want the interior edges on the top surface to be filleted, I want them to remain at 90 degree angles as I’ll be enameling in them after I turn this into a cast piece of silver (or gold if the design is successful).