I wonder if those big plastic bins could be improvised to work as a locking "trunk" on a cart? Maybe they could be placed either on the back seat or back step and with a bicycle type lock, locked to the frame? I have seen them that look sort of like an old footlocker, a lot smaller, of course, and hinged with a flip down lasp over a "u" bolt. If that could be bolted to the frame, then a small lock through the lasp, that might work, and it's waterproof, light weight, and affordable.
Might be a good start to correcting a difficult problem.