What I would generally do in such a situation, is trim and clean up the fillet surfaces that Rhino proposed (red) for some a continuous “band” or “strip”. Then I would explode the closed polysurface and trim away relevant parts to fit in the strip of fillet surfaces.
I’d lay off the boolean, premature joining, and FilletEdge, and then use FilletSrf, first primary fillets, then secondary fillets, which works well, as @Jim has shown countless times over many years.
What do you consider a “primary” and what a “secondary” fillet?
Edit: I’ve tried FilletSrf, but it essentially produces a very similar result to FilletEdge, in terms of generated surfaces. I still don’t know how to solve the situation above.
What’s happening there is that you are trying to make the fillets cross over surfaces that are not tangent. The underlying surfaces need to be tangent to get the fillets to connect (be continuous).
If you first fillet between the surfaces that are not tangent then you can get a continuous fillet string across everything. FilletSrf_example.3dm (1.6 MB)