That really stinks.
I would contact all renters and advise them of the theft and advise that you will be reviewing all outside security footage from last dozen renters to identify culprit - and police will then be involved. If it is returned before you review footage just ban from renting to in future - no police involvement.
As I write this, I wonder if I was a renter would I be pissed to get this. Nah. Because I didn't do it and I'd feel bad for you. But understood if you didnt wan't to take this route with customers.
Good luck!