Two New Yorkers spending a fortnight in your house for consideration (albeit that the consideration is a house swap) I think constitutes a period of absence.
I disagree again. Apart from a suitcase full of clothes, all of the person's possessions would remain in the UK house. The person would not notify bank, building society, doctor, dentist, utility companies, BT, family, friends etc of a change of address. Remember that "temporary occupation does not make a man resident", so it follows that temporary absence (of similar duration) is unlikely to constitute S223 absence.
Just as it would if you were to leave your London house and spend a year travelling the world. You could not make your cruise ship cabin (nor your Swiss chalet) a PPR as you would be living there only temporarily, but your London residence you would certainly count the period for which you rented it out as a period of absence.
I can see that this would be a S223 absence, although that acceptance appears to contradict what I said above. But there is some logic. Travelling the world for a year is a relatively long period of time and HMRC could argue "absence". In the same way that living in a house for a year is also a relatively long period of time, and a person could logically argue "residence". It's all about intention.