It sounds like other than interbreeding, all is well between the southern and northern flying squirrel - so where does the war come in? Well, in many areas, the northern flying squirrel is in serious decline. Some of this may be in part due to habitat destruction - remember that the northern is the "finicky" squirrel who needs conifer forests and specialized fungi to survive - and if this habitat is destroyed, the northern squirrel will perish while the southern continues to expand its' range. However, the more unusual issue is that the southerns carry an intestinal parasite, which is unknown in northern squirrels who are not exposed to southerns. When the 2 species come into overlap, the southerns appear to pass this parasite to the notherns, which then alters the ecosystem of the intestinal tract, making this parasite (as well as others which were previously benign to the animal) infectious and resulting in disease in the northern flying squirrel, while the southerns remain unscathed.
So the southern not only has the upper hand on the territorial advances, but a secret weapon which reduces the competing population.
Meanwhile, however, I continue to enjoy the nightly winter visits by this northern squirrel and about 15 of it's den mates. There is no doubt when they arrive by the thuds on my roof and noisy chatters when I have neglected to appropriately fill the feeders for the night. They certainly have learned to exploit a screened in porch on the house and appear to delight in triggering my trail cameras in mass.