So we have entered dog territory, which is identifiable due to our increased use or rural backroads. We now have at least several dog encounters per day (an "encounter" being defined as when a loose dog comes barking and running towards us). Both Shira and Rachael have had dogs bite their bags and I have sprayed two dogs with the pepper spray.
The good news is that we have defensive weaponry and are getting increasingly good at anti-canine tactics. Each of us is equipped with pepper spray and bamboo stick (see picture). Of course, we also all are able to shout and kick at errant dogs as well.
As far as tactics, we have started using military tactics to defend. In risky areas, we ride in convoy and look/listen for dogs. When one is sighted (or, more frequently, heard), we call out the vector of attack ("Dog left!"). If we are changing tactics from just biking, such as stopping or engaging the dog, we call that out, too. This communication helps us identify and respond to dog assaults.
As to the exact actions, it depends upon the situation. Most loose dogs don't want to do anything more than run to the edge of the property and bark at you. While this can be a bit worrying, it isn't really a problem. We have also encountered lots of dogs that will chase you down the road and have encountered 1) spots with dogs coming from both sides of the street, 2) areas with continual loose dogs house after house, and 3) packs of dogs up to 10 in number.
Our responses range from yelling (which sometimes helps), stopping (which does a lot to make the dogs less interested in chasing you), taking out the stick and raising it (most dogs really do not like this and will turn around and run away), and the pepper spray (which is effective but difficult to use accurately).
We also spoke with two postmen who both said that dogs were a problem for them, but that pepper spray was very effective. They also both told us that the real problem is the dog that you don't see - that's the one that is going to bite you.
For those biking this route in the future: The dogs start in earnest after Fulton, MS and run at least as far as Waverly (where we are now - I will update this as we go further). I suggest getting a stick (bamboo from a side of the road bamboo stand is good), as this is very effective when combined with stopping your bike as a deterrent.