All three of the libraries that you mention (backbone.js, spine.js, knockout.js) are aimed at single-page browser apps.
But your description of your problem sounds more like a formatting issue, not data management. Ie, you want your page to show the data. You don't need to save changes from your page back to the server; your users will refresh to the page to show new or different information.
If my understanding of your goal is correct, I'd go with jQuery or YUI. The libs you mention would be overkill.
Added YUI has a nice treeview widget that supports lazy-loading of branches. I use it for that.
If you do decide to use a model layer, YUI 3 includes Model and ModelList. They're based on Backbone api.
Re: MVC comment In a comment, the OP mentions "multiple views on the same data, change propagation, and edit detection (if a user changes a number) and updates from the server"
For those cases, yes, these days many cool kids are using a complete MVC framework on browser itself. If you wish to go in that direction, then you could use any of the three you mentioned. Notes:
Backbone, and probably the other two, do not provide complete MVC. Rather, Backbone supplies the Model & Controller portions, especially the Model. It is common to use Mustache for the View. In addition, it is common to use underscore or jQuery to supply basic facilities. If you Google for backbone examples, many of them include jQuery.
Checkout YUI new y.App. It includes all of the MVC parts in one well documented lib. y.App is in hot development and is based on the Backbone api. A video-cast
MVC Frameworks on the browser are brand new. Don't be surprised by quickly changing library code, inconsistent docs, few examples, etc. You should also consider documenting and posting your investigations. For extra credit, get it working well on mobile browsers.
49 Signals was rumored to be working on a browser-side MVC framework, but we haven't seen anything yet.
I believe that backbone is the most senior of the Model libraries. But it has proven to be confusing to many new users, hence some of the other libs based on its concepts.
Based on my experience with YUI, their Y.app will have the most consistent and complete api set and the best docs.