@Ravells -- My sanity thanks you for the encouragement, as I keep wobbling back and forth between "It doesn't exist!" and "It does exist!"

I keep finding interesting things that are kindasorta what I was hoping for, but after looking at as many images as I could in the past few days, I'm leaning towards the belief that I'm remembering one or more illustrations from fantasy or historical novels, rather than a real thing. For my purposes, though, real doesn't matter!

My sanity and I have decided, however, that since my project contains different continents than our earth does, that of course their map projections would be interrupted in a different manner, and even of course that would make them think of different ways to logically project their world. So, if I want to, I can darn well make up my own method, although the more I look at it, the more I like this type of thing: mp_Nicolosi-s60-e.png
I think I will play with that, and see if I can find some way to interrupt it a wee bit.

Now, I'm off to find software to help me play with continent placement. Luckily for me, the husband is an EE/mathematics PhD with the latest version of MatLab, and scaaaaads of experience using it!

Oh, and the reason I haven't posted sooner is because ever since my first few posts, I've been spending all my spare time on the wonderful Progonos website! Thank you all for your help.