In this kind of map, sorry but I think you'd win by going as 4 on one lane and push it, why would anyone chose an irradiated pathway? It's like self-defending.
Maybe using your idea but in a more situational way, like a map with hazards, like meteor falls , lightning storms , torrential rain , snow tempests , cyclones , volcanic eruptions or nuclear surges depending on what kind of planet you're on. And you could build some adaptations for your units to these, considering the forecast of the surroundings. (like humans could take cover, while cyborgs could be build in resistant material)
And there are several ways these could be predicted, i mean, you could have a timer set at the beginning of the game (i'd rather everything to be random, and not defined times like at 5 minutes then at 10 minutes etc...), or a warning 30 seconds before it happens or just make it happen instantly, hence being pressurized by the weather as you try to win your lane as well.
Finally, these disasters, instead of dooming a single lane could apply randomly (but again it depends on how you build the map, e.g. if you put a volcano in the center, then it should affect it more than the sides, but if you make a map swept by reccuring meteor falls, it can be global).