Here are some thoughts from someone who owns vacation property:
Don't expect great results from newspaper ads, Facebook, Craigslist, etc. It's too impersonal. Every vacation homeowner that I know, myself included, are very protective of our homes. There's no way I'd ever hire someone off the internet and give them access to my second home when I'm hundreds of miles away.
Avoid homeowners who use a management or rental company. Those companies have cleaning crews, because they're weekly check-in/check-out times are generally very structured. In my vacation home area, the renters flip on Saturday. Check out at 10. Check in at 4. During those 6 hours there are dozens of cleaning crews flipping hundreds of homes.
I like the idea of turnoverbnb. I'd never heard of that site. If it were me, though, I'd cut out the middleman and get on BNB and email the homeowners directly. This makes it more personal.
Be persistent and you'll get an opportunity. Once you do, go above and beyond. Don't view it as your first job but as an audition. Absentee homeowners in a vacation spot know each other. We're the ones there in the off season making repairs. We're the ones there after a hurricane checking on damage. We all have our neighbor's cell numbers, because if an owner is in town and sees a house with a busted window or a leak under the house or a renter acting like an idiot, the owner is notified. It's like an unwritten code. We all know we can't be there full time, so we all look out for one another. Earn the trust of one and word will spread quickly.
There's always a few homes occupied year-round in any vacation area. Try to meet those people. They usually know more offsite homeowners than anyone else does. They'd be your best networking ambassador.