The map generator over at https://donjon.bin.sh/world/ has a fun element where it can convert the map it generates into a variety of formats such as Mollweide projections, Mercator and even spinning globe.

I'm looking for the exact same function, but with the ability to use my own maps. The closest I've found is maptoglobe.com which is fun but "only" allows me to paste my custom map onto a 3d globe.

Does anybody know of a program or app that lets me use my own map images but will convert it to, say, icosahedral for me?