For info, with the image posted at the top of the thread and world size specified, then the scale of the map at Y pixel positions are as follows:

At north pole there is no scale.

Y=125, Scale=313 in m/pix
Y=250, Scale=625 in m/pix
Y=375, Scale=933 in m/pix
Y=500, Scale=1236 in m/pix
Y=625, Scale=1530 in m/pix
Y=750, Scale=1815 in m/pix
Y=875, Scale=2089 in m/pix
Y=1000, Scale=2351 in m/pix
Y=1125, Scale=2597 in m/pix
Y=1250, Scale=2828 in m/pix
Y=1375, Scale=3041 in m/pix
Y=1500, Scale=3236 in m/pix
Y=1625, Scale=3410 in m/pix
Y=1750, Scale=3564 in m/pix
Y=1875, Scale=3695 in m/pix
Y=2000, Scale=3804 in m/pix
Y=2125, Scale=3889 in m/pix
Y=2250, Scale=3950 in m/pix
Y=2375, Scale=3987 in m/pix
Y=2500, Scale=4000 in m/pix

And it reverses again down to the south pole. So treat Y as distance in pixel from the top or bottom of world image.