Challenge: Deglaciated Antarctica in WorldA

Challenge is in the title to prevent confusion with this being any sort of complete project.

Hello!! I'm crowdsourcing this problem I'm having because I have no idea how to achieve it despite being willing to put in the work. Basically the goal I want to achieve is to convert this deglaciated Antarctica onto the objectively frustrating albeit most common pixel format - the NextGen WorldA projection. I feel like its a well overdue patch for the community given the prevalence of sea-level change/Green Antarctica timelines as a trope.

This project is something that bits and pieces of work have been done on before so I'll track a lil history of what I've found so far.
My major problem is I'm not versed in GProjector/projection mathematics enough to convert any of the exist polar projections onto Robinson. Even then, WorldA isn't a pure projection as far as I know so that would require even more manipulation (this step I'm reasonably confident I could do myself). To be brutally honest, I could just trace a guess! But that wouldn't be any fun really, so before I resort to that I thought I'd ask for help. Any pointers, assistance or thoughts are much appreciated.