Here's an idea. Have you got any of that Rubbermaid lid left? I guess any chunk of plastic or even thin wood would do. Cut a piece just slightly narrower and as high as the basket. Either use bungee's or cut four holes in the corners and use clips. What you do is use the board to push your load forward, compressing the actual size of the basket. You could also use the divider to create a separate section for fragile stuff.

I've been wanting foldable baskets for ages. I love the idea of having a lockable top. How are they for weight?

I'd also second the idea of adding a front basket to even out the load. Even a cheap handlebar bag would help.