(Some people are more knowledgeable than me, so correct me if I'm wrong)

You are correct. While it is very easy to change the projection if the default one is equirectangular, retroprojecting to equirectangular is based not on mathematics but purely on approximations. Thus I would recommend to change the projection only after all the important modifications are made since it's very hard to go back.

I use mainly Gprojector to change map projection. Using that software, it is possible to only project a partial section on the map (I don't know it that is also possible with ReprojectImage). So if I want only the missing part of the continent, I crop the image to take only that portion and indicate the coordinate while loading the image. That circumvent the problem of having a file that is too large to handle. BTW, Grojector also has similar limits to the initial file dimensions. 5000px x 5000px is close to the maximum my computer could handle with the software.