How can I export aligned equations to $\LaTeX$?

Question

Using Palettes -> Writing Assistant -> Math Cells, you can enter aligned equations such as:

Cell[TextData[Cell[BoxData[
 FormBox[GridBox[{
    {GridBox[{
       {
        RowBox[{
         RowBox[{"f", "(", "x", ")"}], "=", 
         RowBox[{"expr", " ", "1"}]}]},
       {
        RowBox[{"=", 
         RowBox[{"expr", " ", "2"}]}]},
       {
        RowBox[{"=", 
         RowBox[{"expr", " ", "3"}]}]}
      },
      GridBoxAlignment->{"Columns" -> {{"="}}}]}
   },
   GridBoxItemSize->{"Columns" -> {{
        Scaled[0.96]}}}], TraditionalForm]]]], "Text"]

But saving as $\LaTeX$ yields equations that are unaligned and uncentered!

I'm looking for a SaveAsLatex function that would correctly export human readable code for the following things:

1. (marker) Aligned Equations
2. Hyperlinks (refs, labels, etc...)
3. ItemNumbered cells
4. Centered math cells
5. Numbered and captioned tables/figures

Here is a sample notebook to test your code.