How the "Schoch + Maier" theory can be tested

I start to think that the theory of Jacob Schichenmaier (1861) on the origin of our family name can be adequately true. Today I'd like to demonstrate how we could test it. I stumbled upon an example of the origin of another family name whose history looks pretty similar to the our one.

Well, there is last name of the "Schaichmaiers".

Their family history can be traced back to the place where they definitely come from: it's Holzgerlingen.

As you can see, the area is next to places where our forefathers had lived. 

The genealogists are very happy about that family name because its origin had been attested in the town history on the basis of "urbanonyms" (placenames within a settlement like street names, square names, etc.). 

By the end of the 15th century, the first street names can be already found in the town chronicles. Besides, Altdorfer Gasse, Dietzengasse, am Eschelbach, Glemat (= Klemmert), Stauchgasse, Kelter, Bainhus, Siechenhaus, am Kreuzerwasen, a Schaichhof 

can be seen on the street map in 1495 as "Schayen Mayer" that later will be written like "Schaichmaier". I think this alloy of two names is more than just interesting for us. What if our family name had been built in the same way? 

Of course, we don't have any idea whether Schayen Mayer meant "Mayor of Schaich" (occupational surname) or just "Schaich + Maier" (double family name). 

Schaichhof in 1930s

But what about Schaichmaier in the quality of family name? The very first Schaichmaier I found was attested in the 16th century: 

If Johann Christoff Schaichmaier was born in 1596, so his father Hans Schaichmaier should be born in 1570s. 

Let us notice that in 1495 it was spelled as Schayen Mayer and in 1570s we already meet probably one of the first Schaichmaiers. The gap is about 60-80 years only! Thus, I conclude the fusion can happen relatively fast and the same could take place in the case of the Schochenmaiers.