Hi Harvey:Your tree shown in The forth pix have totally different leaves compared to Col de Dame cultivars be them White black or Gris.
Your fruits look similar to Col de Dame,I had here but we have to take in consideration,that Socorro black in your place might have caprified fruits,and That is why they look similar to uncaprified Col de Dame.
I have seen your Whole tree in another topic,and ,it has different leaves.
Note:The fig confusion,is prevalent,for the reason,that some people describe fruits of a said cultivar while caprified,and other from other climates describe fruits,of same cultivar while they are uncaprified.
The difference is obvious,and so,the 2 descriptions are not similar creating confusion.
In My opinion your tree is not Col de Dame.
Here is ,My Col de Dame Gris tree,fruits leaves etc.
The fruits in first pix are ,from about three years back when weather permitted ,to ripe this type of cultivar,because the last few years were very bad for ripening figs here so they did not get ripe.
Maybe this year.