Need a simple reprojection tool

I want a simple tool to reproject a crappy whole-sphere image like this to something nice like Mollweide or Winkel Tripel. It seems like this would be easy enough with gdal, just have to learn enough about CRS to do it. The source looks like Plate Carree, no doubt produced by someone naive with a raster array of lat/lon samples.

Here’s a great StackExchange answer on reprojecting a bunch of tiles that’s more complicated than I need.

Edit: Mike M. to my rescue. He saw my blog post and offers

1. Turn the raw JPEG into geodata by creating a VRT file with a projection and an extent.
gdal_translate -a_srs EPSG:4326 -a_ullr -180 90 180 -90 -of VRT moon.jpg moon.vrt
2. Reproject the raster into the projection you want.
gdalwarp -t_srs EPSG:54009 moon.vrt moon-moll.tif
I chose projection 54009 based on a simple search for Mollweide on Spatial Reference, finding this: VRT is an XML-based format that leaves the original JPEG untouched:
I should turn this to a single-serving site. Upload a Plate Carrée, download in one of several tasteful projections.