This is a truly astonishing construction. I'm a bit pleased with myself for getting as far as I've done, given how little math I encounter in my life. I have a complete grid and a complete first sequence (my mind reeled when I realised how the sequence completes).
I'm not asking for overt help, just generally curious whether or not there is a more elegant way to determine the remaining sequences than simply trying various other combinations of "parameter" and starting point. At the moment that's what it feels like to me but that seems like it could be quite a slog.