In S.P.A.Z. is it possible to stay in one chapter and collect lots of data to level up before advancing the game, thus not have to deal with any zombies? Or is the zombie attack guaranteed to happen after X number of jumps?
No, there is no time limit. The zombie invasion is triggered by advancing the main quest. However, the really good stuff doesn't really start appearing until later chapters, but I suppose it is possible (though very slowly) to data farm in the early chapters to pump your research.