My thought is outside of an isolated bark now and then, barking any time of the day is not acceptable. I have owned dogs while living in town and felt like an a** even when my dogs barked at unordinary things (fire trucks, hot air balloons, ect). A shock collar and a "shut the f*** up!" out the window have cured all my barking problems. Unless someone is breaking into my house or walking around in my back yard in the middle of the night, I shouldn’t hear my dog.
I'd let the owners know that it’s gotten out of hand, give them a chance to address the problem. If they don't after a week or so remind them they have 2 more days to solve the problem and the cops will be called next. After a few $90 (around here anyway) tickets they should get the picture. It’s always unfortunate when you have to involve the police with matters like this but if your neighbor is rude enough to not care that their dogs barking is disturbing your peaces, then they are most likely a neighbor to not have on your favorite neighbor list to begin with.
I have sorta a similar problem; we have a cat that likes to tour the neighborhood. We recently moved and only know our direct neighbors but none of them know who the cat belongs to either. They also have the same complaint, the SOB chits whenever, wherever. I stepped in one of its bombs mowing the lawn this weekend and also noticed a few nuggets in our garden beds and the one that pi**es me off the most, our kids sandbox. The last thing I want to do is see Sally and Tommy putting up “have you seen whiskers” posters, but if I can’t find the owners that might be what will happen. We had a few cats go missing when I was growing up and I turned out just fine.