Welcome to New England! The Maine gardening forum is often kind of slow, so if you don't get answers you are looking for you might try the New England forum which is fairly active.

How large an area is this and how steep is the hill?
Do you know the zone? Maine covers a lot of zones; you can use the map linked below to find your zone if you don't know.
What is the pattern traffic like? Do you walk anywhere across a broad slope, or are you more likely to walk in a narrower band?
How much sun is part shady? Is there enough sun to grow grass?
Would you consider adding some shrubs to focus where folks walk and then adding some rustic steps or water bars to help divert the water?
Is it possible to divert some of the water before it gets to the slope with a swale to reduce the flow down the slope?
Here's a website from the Maine DEP that has a bunch of different suggestions for erosion control and plants for use with lakefront properties such as infiltration steps and water bars.
http://www.maine.gov/dep/land/watershed/materials.html

A photo or two that includes the area in question as well as what is above and on either side of the slope may help answer some of my questions.

IME there aren't many ground covers that will take heavy foot traffic that will also tolerate part shade and high water flow, and if you walk here regularly, it may be difficult to get something established. There are shade grasses that might work, especially if you could keep folks from walking on one part of the area you are working to establish for a full growing season, so that one year you do one part, and the next year you do another part. We have a sedge that grows wild in areas of mostly shade to mostly sun, Carex pensylvanica. It will take occasional foot traffic when established, but not heavy foot traffic, so you would also need stepping stones. You would want to get flats of plants if you decide to go this route. I don't know if the place below sells to the public if buying in quantity, but I imagine that there are native plant nurseries that sell in quantity.
http://www.northcreeknurseries.com/plantName/Carex-pensylvanica-

Partridge berry AKA Mitchella repens is another native groundcover, but like the sedge wouldn't want regular traffic and would need stepping stones.

Here is a link that might be useful: Maine plant hardiness map

wintergreen is pretty tough but is slow to establish and might not like to be stomped on continuously. look around the boat launches in the area. there is a low growing ground cover that is tough as nails. i think its a evergreen w/ small mouse ear like leaves. don't know the name but its very drought resistant and grows in rocky poor soil areas. theres a lot of it on cadillac mt. in acadia natn. park. maybe pick some and transplant. good luck!