JModelList is for listing items.
To display create/edit form and save item, you need to use JModelAdmin.
However what you are trying to save is not "an item", so you could use JModelLegacy. Using JModelList here is not really a big issue, it still works but I prefer JModelLegacy.
You post your values to a controller, the controller get the values and save, after saving it redirects you to another view or the same view.