I've got a couple buddies who are county sheriff deputies. You're pretty much spot on in that you're not going to get any help from law enforcement...
You've got three strikes against ya:
1. You left the saw sitting in a yard.
2. You have no proof it was stolen.
3. You have no proof that this person has it.
The best chance you have of getting the saw back is to be up front and honest with this guy. Tell him there's a REWARD for the return of the saw.
Beyond that you are out of legal options to get the saw back.
We had an expensive riding lawn mower stolen from the shed at our flying field years ago. We knew who took it but had no proof, so the cops couldn't help us.
Remember, INNOCENT UNTIL PROVEN GUILTY. Even if this guy is guilty as the day is long, we can't throw that principle out the window because it just might come in handy for you some day.