I suspect that blackspot infects only the green canes, not the old barky ones. Also, I think infections on the canes would be nearly harmless except as reservoirs for infecting the leaves. They are important sources for inoculum if the plant has been defoliated and especially when growth returns in the spring. I suspect that spraying the canes with antitranspirant would greatly reduce the release of spores from these lesions, but that hasn't been scientifically vetted.

If you spray weekly with mancozeb or another good fungicide, it should greatly reduce new infection. All the infections are local, not systemic. Cutting back part way would probably improve the plant's appearance for the fall flush, since new growth is going to come from the tops of naked canes.

Fred is highly susceptible to blackspot in my garden (also to thrips).

It is a little late in the season to cut it back too much, IMO. Our fall flush is just about over.

Frederick can live even if you cut the canes back severely over winter. My FMs aren't real happy when I cut them back severely for shaping, but they do survive.
Can you try spot treating the cane problems?
One thing to watch for....are the spots on the canes dark black and actively spreading? If so, it may not be BS and you may need to remove the canes to save the plant. Watch the spots and see if they're active.
I've had two different cultivars with large black spots (with a hint of purple) and have lost roses to whatever it is; cutting back below the black and cleaning secateurs and then recutting even lower saved two roses.

When is the rose-stopping frost for you guys? Around Nov 1? It might be too late for post-pruning growth to produce bloom, but it would be important at least to get some healthy leaves on there to help the rose prepare for winter. I think of our season as similar to yours, but a little longer. Here we probably still have time for another full cycle of growth and bloom.

My fall flush is just beginning--different microclimates, I guess, in New Jersey!--and interestingly, Freddie has lots of leaves. They get spotty, the canes are spotty, but I lose very few leaves. Most leaves are speckled, the canes are speckled; Diane, I didn't get around to calling out the troops from the Rose Society--maybe I've got two diseases going on. . ..

This rose wants to grow and grow. I don't know how you can keep it happy in a container. If it's root bound, you need to repot it. When healthy this rose is very disease resistant.