I'm finding myself in a similar boat. I canceled within 12 hours of booking, with an owner (who has a "Strict" policy), for dates that are months away in August. The booking was a human error-- I was tired, I booked hastily, and then had second thoughts.
Now she's got about $250 of my money, which is hers by right because airbnb allows the "Strict" policy. All I can do is ask nicely, that she please make an exception and return it.
The airline policy that requires airlines to issue a full refund for a 24-hour cancellation is actually federally mandated. Airbnb might consider such a policy in lieu of the "Strict"-and-up policies, so that there is room for human error in this process.