Adding to the excellent advice you got from wildscaper, let me add that soil amendments will do wonders for your recovery. If you've had a mud situation for a time your soil is already compacted from rain, so mulch will go far in allowing it to loosen up but a dose of molasses and cornmeail along with Medina Plus or Soil Activator will prepare your soil to enable the plants you bring in to thrive.
Planting ground cover or any plant in hard, compacted soil is introducing unnecessary challenges to your project. Start with preparing your soil with these excellent, affordable amendments, give it shelter with a mulch (hay or straw is inexpensive and effective) and then plant sections at a time so you don't get overwhelmed. Mulch first, because if you plant first, you'll cover up some of them and waste your time and money.
The best news is that we are coming into the season when it's the best time to do this! Perennials do best when planted in the fall and allowed to grow a good root system before the spring entices their tops to grow out. You can plant rye grass but unless you want to mow every winter make sure it's annual and not perennial rye. Good luck!
Kathe