On the subject of the Set trying to breed a Mistborn... that makes no sense whatsoever. To date, the Set have been doing two things: amassing funds and kidnapping women with allomatic bonds. However, given that it's been 10~ generation since Spook's generation, the odds of getting a Mistborn are entirely unlikely. It was clear enough in Mistborn that Mistborn are a once-in-a-lifetime deal, and that was with hundreds of thousands of skaa. With Elendel's far lower population, the odds are incredibly unlikely. Plus, the Set is most likely made up of middle-aged men, so they most likely will only survive for another generation. With six women, one generation is not enough time to get a Mistborn.
However, assuming that allomancy works as a recessive trait, and what with the rise of technology, there is a chance the Set does know something about allomancy that the rest of don't. However, I'll bet that it does have to do with Hemalurgy. Living forever has always been sought after, and Marsh has been around for three or four hundred years. If they have access to Atium, they could be trying to get themselves to become immortal. As well, that stand with the atium was empty in SoS...
Edit: forgot the address the funds. Odds are, that's going to be used for something less than nice. Given how rare various metals are, they could be trying to get their hands on some of those rare metals.