This is not going to be a technical blog, but just in case anyone out there is searching for a way to do this, I thought I'd share the solution I found. It may look like Squarespace 6 only provides a single sidebar that is shared by all your blogs, but there is actually a way to get around it - you can use custom CSS.
The basic principle is to add blocks for all your sidebars all together in one place, and then turn them visible or invisible based on which page you're looking at.
While editing your blog, if you go into Style Mode (the brush icon in the lower-right hand corner), you should see a CSS button appear in the lower left corner of your browser. This lets you add custom CSS to the top of all of your pages. Here's the CSS I added:
#block-99e6fe148f38135539c0 {display:none;}
#block-a178391d0910821e59b1 {display:none;}
#collection-504c031ae4b087270c53d8e3 #block-a178391d0910821e59b1 {display:block;}
#collection-504b5b47e4b00e2aa82c8546 #block-99e6fe148f38135539c0 {display:block;}
.collection-504c031ae4b087270c53d8e3 #block-a178391d0910821e59b1 {display:block;}
.collection-504b5b47e4b00e2aa82c8546 #block-99e6fe148f38135539c0 {display:block;}
The first two lines turn both sidebars invisible. The next two lines turn the respective blocks visible when you are looking at the correct blog's main page. The last two lines show the correct sidebar when you are looking at a subpage of the blog (solo post, comments, etc.). The main trick is to figure out how to get those horrible looking numbers that represent the sidebar blocks and the blogs. If you use your browser's "View Source" capability, and then search for the <sidebar> tag, you should find an id attribute that looks similar to the "block-#####" ids above. The "collection-#####" ids represent the blogs themselves - if you look at the blog's <body> tag, the id should be in this format.
Hope this is helpful to someone!