This is a solution of sorts to the problem of the serialization of nested lists. It really only works for my specific case, but I think this case might show a need for some changes to the jQuery UI Sortable tool.
This solution works by redefining $.ui.sortable.prototype.serialize to something I can use. It doesn't change the API or mess with the original source code. It would be real problem if I needed this and another sortable on the same page...
(The serialize button logs to the Firefox console if it exists or just does an alert if the console doesn't exist.)