Incase anyone really does want to do this: http://www.gdal.org/gdalwarp.html is awesome.

But he had the map data and the text data all compressed into a single image -- the text would have been warped as well.

Hopefully someone will find it useful for the reverse, warping an overlay image to place on top.

Jason Davies has done excellent work on addressing this problem in the browser https://www.jasondavies.com/maps/raster/

Except, that's also going to screw with the nice 4pt fonts he talked about...

He chose Mercator source data.

I can understand why someone wouldn't want to set up their own tile rendering system (and hence not use something like OSM with whatever projection they want), but it likely would have been less work than screenshots.