I take back what I said about Slaine being an idiot without any plans whatsoever. Dat move was brilliant.
If he just killed Saazbaum back in season 1, he'd be on his own even if nobody found out. Since he was "Cruhteo's terran", nobody would trust him at all and that way he would have no allies whatsoever. Hell, they'd give him the bullet and put some other knight into the Tharsis. But if he saved Saazbaum AND got Lemrina imitating Asseylum, things start getting different.
All he had to do was take his sweet time, earn himself the right to suceed Saazbaum and then somehow get him killed. The battle against the terrans was the perfect opportunity for that. Inaho and his orange kat are well known for bringing down the Diouscuria once already (and probably more martian kats than the United Earth forces combined).
Also, if he fired the shots like that around the earth, who would notice? On the radar they'd look like high speed debris and the only one knows about where they came from are Slaine and Harklight. Which means the only guy who can blow his cover is Harklight who did the calculating. And Harklight is unlikely to do that for a number of reasons:
1) He admires Slaine due to their similar situation (both didn't have an easy start with the martians)
2) Slaine's ambition is also his dream- have a better society on mars. If he were to sell out Slaine, that dream would collapse.
3) He's the guy who took care of the aiming. If it came down to it, Slaine could claim Harklight manipulated the data so the shots would hit Saazbaum instead of Inaho. And boom, all the blame would fall on Harklight while Slaine could use his newly-earned position as "Count Slaine Saazbaum Troyard" to get the suspicions off himself. Furthermore, as Slaine stated, the foresight of the Tharsis can't see that far into the future so they would believe that he "wouldn't have known"