Native grasses and dogs
I have a heavily sloped area, partial to full sun, with heavy dog traffic. I'd like to find a native grass/groundcover that will establish itself in spite of all of the canine competition and abuse. Any ideas
A low native grass or groundcover will not be able to tolerate heavy traffic from dogs. You can plant taller native grasses, but you'll have to cage them to protect them from getting trampled as they get established. The online publication, "Native Plants for Wildlife Habitat and Conservation Landscaping" has a good section on native grasses, with color photos and a growing requirements chart.
If you have heavy dog traffic, you'll do well to get anything established there. You may have to use a combination of paving and mulch, landscape timbers (or similar) to create beds and terraces, and possibly some tall fescue (which is not native. ) Aim to establish paths for the dogs (they are creatures of habit) and discourage beds and other areas with low fencing or raised beds.
You may need to divide your yard in half and restrict your dogs from going into the area where you are trying to establish plantings and then work on the other side. For lawn grass, the best times to seed are late summer-early fall to late winter into early spring. If you have dogs, you may find that you need to overseed in the fall as a general practice.
Here is a good article on lawns and dogs https://web.extension.illinois.edu/hkmw/eb285/entry_9338/