Marble stains are embedded within the stone and not on the surface. There isn't a product that can remove marble stains via conventional surface cleaning.
But the procedure is easy and cheap. It just depends on what is actually staining the marble, but all that is explained in the e-book.
For marble polishing (after all stains removed) you can use the Marble Polish / Etch Remover IF the marble was orginally polished and it is still smooth.
The original finish may have been a "honed" (matte) finish, so you wouldn't want to use the above polishing product on this type of finish.
Unless, of course you want to make the surface shiny. If so, then your best bet is to hire a marble repair and restoration pro to re-finish the headstone.
The DIY Polishing Product above is really meant for restoring the shine on small areas and spots that have been damaged or etched... again on polished marble, travertine or limestone.
It will make a honed surface shiny, but it takes quite a bit of skill to polish a large area with an even shine vs. simply blending a spot into the surrounding shiny surface. That's easy.
If the marble is somewhat heavily weathered and/or rough, then polishing won't work to make it shiny anyway. A pro is needed.
The shiny smooth polished finish is created on the stone by using special abrasives and tools or on a big machine at the factory and not simply by applying a potion or lotion.
Similar to sanding wood. You can't make a piece of firewood smooth simply by staining it. You have to sand it down to make it smooth.
So, the method used to polish the marble will depend on the condition of the marble surface after all cleaning is completed.
If smooth and somewhat shiny... then use the DIY Marble Polishing Etch Remover product.
If honed or rough, consider calling in a stone repair technician, or just leaving it.
Weather will continue to wear on the surface, so you may not want to put too much effort or money into creating a perfect finish. This is particularly true of a polished finish. A polished finish will wear away in time without continual re-polishing.
By "commercial compresses" I assume you mean that you attempted to draw out the stains using different types of chemical pastes.
If not, then do try to remove the stains following instructions in the How to Remove Stains in Granite & Marble e-book (link in previous question). Try using bleach as the chemical in the poultice paste.
Although, given the extent of staining and deterioration, it may be best to call in a marble repair professional skilled with statues.
It does appear that the marble statue has a lot of embedded stains from accumulated paint, dirt and grime. The staining is so extensive (and possibly deep) that professional re-surfacing of the entire statue is probably the only way you will see desirable results.
Of course, this is a job for someone with the very specialized experience needed to maintain the original integrity, lines and shape of the marble statue.