Hi
That is an awful lot of caustic chemicals for a sun baked clay to have endured.
Tim will provide the expert analysis but this is what I would recommend.
Remove all residues from the saltillo using a striper based on Methylene Chloride (Jasco makes one). This can be some nasty stuff so vent while using, were proper personal protection gear, and when you dispose of the residue do so within strict accordance to the guidelines set forth in your community.
Once you do this the, saltillo needs to be washed with neutral cleaner like the TYW cleaner sold here. This may be done several times.
From that point I would determine how much damage the saltillo has. Some areas may develop bisters known as "lime pops".
This is the point where you decide to use a finish that will change the appearance of the saltillo or just enhance it.