Okay, I wouldn't say that I am set in my ways, just that I've tried everything else and I know what works and what doesn't. Let me recap the process one more time, with a little extra explanation thrown in.

In my neighborhood, if I have a problem dog, I will catch it and take it to the local animal control authority.

If the owner of the dog subsequently recovers their pet, and the dog becomes a problem again, I will catch it again and relocate it out of our ACA's jurisdiction. ACAs in other jurisdictions will not accept animals from people not residing in their jurisdiction. Now I have a choice; I can take the animal back to my own ACA, I can put it down myself, or I can release it in the out of town jurisdiction. I know the outcome of taking it back to my own ACA, and I am no longer in the business of voluntarily putting animals down myself, so I am left with only one other choice. I release it in an area in the out of town jurisdiction in a place where it is likely to get picked up. It is not a 100% sure thing, but it is better than the other two alternatives.

Does anyone have a better suggestion? I keep seeing people tell me to turn the dogs in, but where? Our ACA will keep giving the animal back to the owner as long as they are willing to pay the fee, and the dog doesn't appear to pose an immediate threat (non violent manner, no apparent illness).

Yes, I agree, I would also prefer to drive the owners 50 miles out of town instead.

Maybe I need to work on those communication skills a little more.
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The ultimate result of shielding men from the effects of folly is to fill the world with fools.
-- Herbert Spencer, English Philosopher (1820-1903)