Creating custom CRS from existing CRS EPSG:22780?

Question

I am currently trying to figure out how to create a custom CRS in QGIS based on Deir ez Zor / Levant Stereographic (EPSG:22780). For this I am working with a map which shows both the EPSG:22780 coordinates and the coordinates of the custom CRS. I have to work with the following criteria:

1. The custom CRS should be specific to a rather small and limited area (see map).
2. The negative coordinates of EPSG:22780 should be replaced by positive and "simple" coordinates (three-digits in pre-decimal position; see map).

The following topo-map, which I had to redact as it is not published yet, shows how the old and new coordinates should correlate:

I tried to figure out how to change the proj.4 parameters of EPSG:22780*, but as I am doing this for the first time and without any guidance I am kind of lost atm.

Here they are:

+proj=sterea +lat_0=34.2 +lon_0=39.15 +k=0.9995341 +x_0=0 +y_0=0 a=6378249.2 +b=6356515 +towgs84=-190.421,8.532,238.69,0,0,0,0 +units=m +no_defs

*(I got these from the Proj.4 library in QGIS and noticed, that epsg.io provides other values for +towgs84 (+towgs84=-187.5,14.1,237.6,0,0,0,0) - in case this is somehow relevant. The other values are the same.)

Answer 1

Looking at the coordinate pairs, it seems that the origin of your local cooordinate system should be at (-356000,-73200).

So you have to set the x_0 and y_0 values accordingly to have zeroes at that point:

+proj=sterea +lat_0=34.2 +lon_0=39.15 +k=0.9995341 +x_0=356000 +y_0=73200 +a=6378249.2 +b=6356515 +towgs84=-190.421,8.532,238.69,0,0,0,0 +units=m +no_defs