Problem Creating appropriate grid

this is my first time trying to create a module and I have a problem I don’t know the best way to solve.

Game is Star Empires by TSR games (c) 1977 and is out of print. it is a 4X space game that can use 4 different scale maps: Star map (exploration), Deep Space & System (either empty or with the Sun and all planets placed), the Planetary Map (only one planet and possible hazards) and finally the Ground combat Map.

My main problem is that the Star Map is on a Square Grid with the Rows offset that represent a hex grid pattern, but the “1 inch” squares are not square, what would be a good way to establish the movement grid?

On top of that there are multiple stars in each square at different elevations from +15 to -15. Ships can only travel from one star to another.

I hope that this is possible, but to me it seems daunting.

RBeyer