I'd be lying if I said a thought sort of along these lines didn't occur to me. ...Still not sure how I feel about even having the thought, though.
When you have Kian obsessively examine the napkin, he accidentally implies he's from the merchant classes. I don't know how much weight to put on a comment like this.
Oooo, interesting. I missed that. *notes for next playthrough* Though I wonder if he means his family that he was born into was of the merchant class...? Or that whoever raised him after he was orphaned was of the merchant class? (What the hell happened to his dad...?)
We're also a little fuzzy on the ins and outs of Azadi society, here. Curious to learn more on that front.
Oh, as I was writing this I had an epiphany of shorts! (warning: it's actually a depressing idea) Assuming again that Saga=April and Kian has Etta and Magnus as parents as well, imagine a long tragic story where: this beloved couple first "lose" their (shifter) daughter and then somehow also "lose" the House of All Worlds, then maybe Magnus gets killed leaving a depressed (and maybe impoverished) Etta In Arcadia with baby Kian until the events that Kian remembers here (Etta jumping to her death from the city walls). 
I explored a similar line of thought, here, but I'm not sure. I mean, Etta is very obviously not a normal human, so I can't see her being able to just hang out in Azadi society. I mean, granted, that in and of itself could be enough to make her want to jump off a cliff, but the whole scenario seems very unlikely. It also seems unlikely that Kian would have been raised in Azadi society, were this the case.
To your earlier points...it's possible. Though how fucking unlucky do you have to be to have not ONE but TWO babies shift away to another world? Also, I'm a little unclear on how shifting works in regards to the HoAW. Lady Alvane implied that April couldn't just shift there the same way she could to Arcadia (I thought...?), but if LA is some incarnation of April, then it might be a moot point.
I'm still wondering if Kian has a connection to one of the other of the Kin. I believe I brought this up briefly in another thread. April's (and Saga's) connection to the White seems much more nebulous and complicated than a simple blood relationship. It seems much bigger, much more a thing in the hands of the universe and the Balance, etc. I'm curious if Kian has something similar going on in that respect. Maybe not even with the Kin. Maybe with something else. I mean, the Six and much of Azadi culture is still very open for speculation. And it's been loosely implied that someone on high has taken a liking to Kian and may have had a hand in his meteoric rise as an Apostle.