Thanks so much for answering! Obviously, none of us know 100% that they're dating. But for the sake of the question, we're suspending disbelief and saying that they are. I'm between two episodes on which one I think was their first time filming RM after starting to date, so I'm curious to see what everyone else's answers are.
I think one part of the 2013 theory is that they were dating by 150. But whether that was the first episode they filmed after starting to date is up for question, so I'm curious to see if people think that is the first episode or something before that.
Spartace in FO: I find really interesting because I feel like there's something subtle there based on YJS's comments. There a few times where YJS teases KJK and SJH about being interested in each other. For example, he observes that KJK can't stop smiling when he's picked to be on the same team as SJH, and when doing chores, YJS gets SJH to shout "heyo" to KJK. In that scene, when YJS shouts, "KJK, SJH has said..." SJH tries to stop YJS from saying something. Obviously, whatever she thought YJS was going to say, he doesn't, because she then joins in the teasing, but I feel like there was some talk about KJK between her and YJS behind the scenes. But despite this teasing, YJS never encourages KJK and SJH to stay together when the family separates to do chores, and they don't interact with each other very much from what we're shown. Perhaps YJS wanted to make a bit of love line between them, but the FO staff wanted to keep the KJK-LH love line alive so nothing came out of it. And since KJK and SJH are still awkward when they meet on RM, I'd say they just met that once on FO and that was it.
As for dating the CEO being a cover, I'm inclined to disagree because, at the time, it wasn't good for SJH to be revealed to be dating the CEO. Obviously, now, we know it had minimal effect on her career, but I know at the time she suffered backlash from MC fans, so if it was intended as a cover, I think dating the CEO did more damage than good. So I think she definitely dating the CEO; after all, we see the letters of his name on her fingernails in ep 126 (filmed December 17), so she was dating the CEO at that point. They broke up some time in 2013, and my guess is January or February, since while we get some MC in 2012 (married couple in ep 113 - though SJH insists they are divorced), they start getting partnered a lot more in early 2013 with the pepero game in ep 137 (March 5).
These are, of course, just my observations. Thank y'all so much for sharing, and I hope more people share their opinions!