You'll have to create your own custom TreeLoader class to construct the node names RESTfully in the url instead of passing 'node' as a param. As you can see from this example code, specifying your own TreeLoader allows you to easily specify the HTTP request method.
root: new Ext.tree.AsyncTreeNode({
expanded: true,
loader: new Ext.tree.TreeLoader({
url: '/sample-data-toc.json',
requestMethod: 'GET',
preloadChildren: true
})
})
Dig into the TreeLoader class and extend it to provide your own url scheme.
EDIT: after looking at the TreeLoader source, it looks like you should override requestData to properly set the url based on the node, and you'll probably want to change getParams to either return nothing or any special query string params you have. Should not be too much work. When you're done, share back your RESTfulTreeLoader with the community!