@Priscilla150
I don't understand your post exactly. The long term cancellation policy automatically applies to any stays of 28 days or more, so would be what was in place for your 30 day booking. There are two types of long term policy you can select from, flexible and strict, but the difference is only relevant to cancellations made before the trip.
If a guest cancels after the check in date, then the same penalties apply. That is, they pay for any nights already spent, plus 30 nights from the date of cancellation or the remainder of the stay, whichever is shorter. Therefore, your guest was not due any refund according to the cancellation policy. The only way this would have happened if that, instead of the guest cancelling, you either altered the dates or accepted a date alteration from the guest. If you do that, the guest gets refunded all remaining nights.
So, in this situation, the thing to do is to tell the guest that they must cancel and the cancellation policy, which was provided to them prior to booking, will apply, but you are happy to refund any dates that get rebooked. Explain also that the host does not get paid until after the guests have checked in, so you will only be able to refund after that, i.e. not as soon as someone books. You don't know for sure that the rebooked dates won't be cancelled too. Wait until the payout has been made.
I don't know how it is for the travelling nurses in your situation, but the ones that stayed with me got a housing allowance that covered their entire stay and there are certainly cheaper options in London if you need budget accommodation (my rooms are not basic), so this allowance seems to be pretty generous.