Looks to me like 2 different peoples used the sites - those that built with large stones/slabs, and those who built with the much cruder small stones of the enclosures, who also used old worn out statues from the slab builders for building material - a common practice later on.
The open mouthed head is reminiscent of 19th-early 20th century fairs that had painted statuary clowns with similar open mouths - toss a ball at it, and if you get it in the mouth, you get a prize.
More questions than answers, as is to be expected with such ancient artifacts.