Since an SVG file is just a simple text file (ok, maybe not so simple, it's XML after all), you should be able to just load the entire thing into a plain text editor.
You state you already know what the co-ordinates should be, and you know the dimensions, so all you need is to figure out which co-ordinates are which in the SVG file and you should be able to manually change them.
The only difficulty you might have is with the path command.
Paths are defined as a long string containing commands such "M x y" for Move, and "L x y" for line.
"M 1 1 L 1 2 L 2 2"
Which will MOVE to 1,1 then LINE to 1,2 and LINE to 2,2
The SVG page at the Mozilla Developer Network is a great reference, to all this stuff:
Once you've adjusted all your co-ordinates, you should then just be able to load the SVG into any package that can load it, and then produce a GeoJson.
QGis 3 understands how to load SVG files, Just use the "Vector" layer in the Data Source Manager:
Beacuse QGis is geospatial aware, it shouldn't change your co-ordinates, and it might even be helpfull by asking you to tell it what your co-ordinate system is.
Once you have your layer loaded, all you then need to do is just right click on it in the layer manager, left click on export, and set the output type in the export dialog as "GeoJSON"