my initial thought was that hyperspace would allow a _shortening_ of the distance traveled from point P0(x,y,z,q) to P1(x,y,z,q). Since I was _really_ into space combat games at the time... that would have been really cool!

However, - and this is obvious when you work through it - when you use Euclidean distance (https://mathworld.wolfram.com/Distance.html - see the General equation), the distance travelled increases, thus obviating a key part of my game, which was to "jump" through hyperspace to shorten the trip. I didn't care to rewrite math enough to make the game work out, and since I'd spent so much time learning math, graphics,and larger-scale program design, I was burnt out. It was a great experience.

One day I might return to the notion, but it'll be around the hyper-dimensionality experience, not as a combat game. I don't like the slice mode of 4D games qua the OP, I far prefer projections from 4D as a way to understand the 4D realm.