Adding some more pictures of the internals. Don't know the proper part names, so I'll call the brass piece that sits inside the shoes the "under-shoes-piece". Here is my guess of how things work with this machine (corrections welcome; this is mostly new to me). When the sprocket (driver) is pedaled forward (by about 20 degrees), the 5 rollers (you can see 2 in the photo) on the driver clutch jam, push out and lock the driver to the hub. When coasting, the rollers are free to roll so the hub spins independent of the sprocket. The piece with the rollers on the driver moves out toward the sprocket (when pedaling forward) and in (when braking) on the threads of the driver, but can only rotate about 20 degrees either way before the rollers jam. In both drive and coast state, the driver is not applying force to the under-shoes-piece, and thus the shoes are not pressed to the hub. The band spring wrapped around the shoes holds them against the under-shoes-piece. The under-shoes-piece also has rollers (2). When braking, the driver moves in and presses into the under-shoes-piece and the shoes ride up on the angled surfaces of the brake cone on one side and the under-shoes-piece on the other side, and thus press against the inside of the hub. At the same time, the under-shoes piece rotates slightly (because of the direction on force from the angled surcaces where it meets the driver) which causes the rollers to jam and lock the shoes to the under-shoes-piece.
I don't have a good feel for how much "rib" should still remain on the shoes. I'm including a side photo of one of the shoes. Is there any sort of spec or rule of thumb on how much rib should remain?
The reason I want to replace the shoes is that it takes a lot of force to stop the bike, the shoes appear to be worn (to my amateur eye), the inner shell of the hub looks OK (but hard to tell) and there doesn't appear to be any adjustment.
Thanks so far for all the helpful input.