Off hand I see a few thing that could be done...
Main part do you want to buy or build....
-A jackshaft, in a 1:1 ratio, with an outboard brake(a mech/hydro disc)...
This might help with the alignment, as it look like (above pics) there might be a slight problem with it...Itll take some work as you have a small space, but enough to work with...could always flip the tire, go right side drive, have the brake on the jackshaft outboard on the drive side... Down side, brakes need the chain to be intact, loose a chain, NO BRAKES....
-Disc on rear tire.
Could use existing sprocket to be the disc, but its performance is hampered greatly by lubricant from chain....
Better to have a dedicated disc for the braking.
Big question will be, Is the rear rim easily to accept a disc being mounted to it? It isnt a live axle so the disc and sprocket need to rotate as one with each other, in the confines of the limited space of the rear part of the frame... This also limits the physical size of the actual disc and caliper that will fit.
-A drum brake wheel... this might be something you may be able to find and that will fit your frame/wheel.....
I personally dont have any experience with these type, but know a few basic's.
-A scrub brake.....
Itll also take a bit of work to fit, but it can be somewhat worthwhile, however at the expense of rear tires....
- A better diagnosis of the current band brake.....
Howabout a look of the assembly with out the guard.....
When was the last time you did any maintenance on the band drum?.....
How does the band react when you apply the brakes?....