The workaround now mostly works, but it induces a few limitations on the doodles. The colours in the browser saves are saved as the #aabbcc form, but without the first #, so it's not possible to export semitransparent lines. The save format is also unable to save numbers beyond [0,520] so the locations to up, left and right of the canvas get squished back inside the canvas, the lines going below the bottom of the canvas aren't affected as they are still inside the range.
I'll check if I can automatically cut off the parts of the lines outside the canvas and post the workaround a bit later once I've eaten and stuff.
The dod browser format saves are also unable to use higher accuracy than 0.5. adding a file with filename "config" and contents "accuracy=2" will make the client use the same accuracy to help avoid drawing too detailed and having it get destroyed in the conversion.
The browser script for loading the file contents to localstorage is available at http://qazhax.herp.io/scripts/. I uploaded a new version of the client here, in the new version ctrl+shift+s saves in the browser format. The saved file can then be dragged and dropped onto the popup created by the browser script and the script will load it into the active room.
I also finally changed the error messages while I was at it.