I have never ever in my life had a problem doing sj.K after anything I do. I'll get instant turbofall maybe 1/100 of the times I try it, even when I first started using her. For that, I think there's a method you're overlooking, and it isn't magic or brute force practice either.
I honestly think it has something to do with when you're inputting your gatlings, and how well you can feel the delay between the hit-stun of a move, and performing a followup. I generally go from 5P into 159K, without any problems. Or 1259K. But I also delay it for a moment, I input 5P, then I input the SJC, then I input K. Steps 1, 2, then 3. I don't try steps 1, then 2+3, which is what I think you might be running into.
Wait as long as possible and try it, go slow and work your way up, that way you understand just how long you have to buffer in your next command.
Hope that helps!