Raphios, a big thank you to you for pointing me towards Alternative World Map Creator. I have been looking for a program exactly like that for ages.

I would love to be able to do what you are asking for as well - take any map in the equirectangular projection and convert it to an oblique projection. Unfortunately, Alternative World Map Creator only does it with its preset world map. I would love to be able to load up my own map in the program, and convert it.

So, it seems we are looking for the same thing.