The guests are already "customers" but can still cancel and the goal is to implement a B2B sales cadence model by calling within 48 hours to offer concierge service to understand the needs of the guest better/upsell services, rich HQ email within 3 days, and HQ letter in the mail with local city guide within 30 days to get the customer within the 14 day non-refundable window and increase customer engagement through attentiveness to guest relation needs.
I think a better question would be to understand why people are cancelling after making a booking?
Are you catering to business travelers whose schedules may change? (no amount of cuddling will save all sales)
Are you catering to vacationers who might find better deals elsewhere? (appeal to their frugality with special non-flexible offers)
Take a page from the airline industry, perhaps simply offer different rates with different options. Cheaper rate is pre-paid and non-cancellable, higher rate has full flexibility.
Then you can more narrowly focus your efforts on cementing the 'flexible bookers' while you've already collected on the more frugal folks.
Feel free to book a call if you'd like to chat.