Hi, 

It does seem fairly compacted, so aerating before seeding or planting would be beneficial. With that much shade, a fine fescue blend would be more successful. The benefit is that you don't need to mow as often either and it looks nice as it gets longer. You will most likely need to aerate and over-seed yearly to keep it thick enough in the shade to outcompete weeds like the stilt grass. 

It's best to perform lawn renovations in the early fall but you can prepare for it beforehand. You can reference our Lawn Renovation page for more information and steps on how to prepare. Starting with a soil test would be a good step to perform now to see if the soil is lacking any nutrients or the pH is not optimal for lawn growth.

You could also consider reducing the amount of lawn space by extending the garden beds. Installing some shade-tolerant shrubs with ground cover or living mulch would be less maintenance over time. You could still have some lawn space in the center or towards the bottom of the hill but this could reduce overseeding and mowing maintenance. 

This spring it may be helpful to use a pre-emergent herbicide to reduce the amount of stilt grass seedlings germinating. You will likely still have some but you can mow it short and keep it from producing seeds before planting any seed in the fall and it should help to reduce its population. 

Let us know if you have questions after reviewing the links. We can help read your soil test results as well. 

Emily