Hi there,
It took too long for my post to get through moderation, so I figured everything out myself before the replies came. I'm on OS X, so I used the various commandline tools.
You're right about orthographic, but I didn't quite describe myself well enough. Anyway, using azimuthal made an end result that looks like what I wanted.
Here's what I did...
I found a blue marble geotiff, and used listgeo to get the data out of it. My map is 10000px by 5000 px. I altered the pixel scale to 0.036 and this turned out completely right (as far as I can tell).
So I put the geo data into the tiff to make a geotiff...
geotifcp -g Roshar-equirectangular.geo roshar_world/roshar_no_title.tif Roshar-equirectangular-unskewed-geotiff.tif
Then I warped it to the azimuthal equidistant projection I wanted...
gdalwarp -s_srs '+proj=latlong' -t_srs '+proj=aeqd +lat_0=-30 +lon_0=0' Roshar-equirectangular-unskewed-geotiff.tif Roshar-azimuthal-equidistant-unskewed-geotiff.tif
Then I opened that in Photoshop and pasted the old map on top of the new one, lining everything up in the middle. I increased the size by 171% to get it to align (I'm not worrying about the dodgy interpolation of data).
Then I saved to a new tiff, copied out the geo data from the azimuthal geotiff using listgeo, then copied it over to my new saved version to make a new geotiff:
geotifcp -g Roshar-azimuthal-equidistant.geo Roshar-azimuthal-equidistant.tif Roshar-azimuthal-equidistant-geotiff.tif
Then I warped it back to equirectangular:
gdalwarp -t_srs '+proj=latlong' -s_srs '+proj=aeqd +lat_0=-30 +lon_0=0' Roshar-azimuthal-equidistant-geotiff.tif Roshar-partial-equirectangular-geotiff.tif
Then in Photoshop I pasted the new version on top of my old equirectangular version, scaled to 58.1% aligned in the middle. And that was pretty much done.
Then I used make_gores.pl from http://www.vendian.org/mncharity/dir3/planet_globes/ to make a gore map so it can be printed out on stickers and stuck onto a globe.