I have several pages on my blog that are quite specific and I know exactly what links I would like to appear on the sidebar of each page.
The only way I know how to control sidebar content is to designate certain asides to appear with certain layouts.
In my case, these pages do not each need a unique layout (per-se), they just need a different set of asides. So I am reluctant to create a separate layout for each page just so I can control the asides with more precision.
You are correct, you'll need a new layout in which you can specify specific page_asides. There's a good example of the customizations you'll need to make here: New Plain Page Layout for Octopress