I know that I'm lucky to be in the guild I'm in with our level of KAM readiness. Most people attempt the mission and the win rate is about 60%, for a total of 22 shards last time. We still have a ways to go to boost our completion percent over 80 and to boost our attempt % up to about 90 (or better, if we can manage it), so there's lots of growth to come, but even 22 is a decent amount. With no growth at all, I'm 7 months away. But I think that there will be growth, and I'm projecting 5 months.
To get it down to 4 months, though, would require averaging 36.5 shards, and I don't think we can manage that. We might end up at 37 shards the month that I get KAM to 7* but we can't average that, so 5 months it is.
So I'll get KAM a month after CAT, and we'll see where my conquest performance goes at that point. I'll probably still have mild struggles with Sith since mine are terrible, but hopefully bosses will get easier & easier as I pick up more GLs + KAM + CAT.