Mats are definitely not cheap but with any significant slope, they are definitely needed. Otherwise, some fast germinating rye or fescue with straw mulch would be your best bet.

How do those 2 grasses do in shade as this is a big part of the problem with getting grass to grow. If the seed doesn't succumb to the slope, then the shade prevents it from germinating properly.

They do OK in shade, but for significant shade, you will probably need a fine fescue blend. See link below:

Here is a link that might be useful: Bonny Dunes FF blend

I use the erosion control mats extensively and they work well. You could even seed now, cover the seed with mat and it will sprout in the spring, thus reducing erosion through the winter.

However, grass needs sunlight to grow. You may be fighting an uphill battle if you are trying to grow grass under a dense canopy.

In my neck of the woods, typically we open up the canopy to increase sunlight on the forest floor. The natural condition of the woods in our area, used to be open canopy woodlands, savannah... but european settlement suppressed fire, creating dense woodlands with highly erodable soils and no ground cover, which is a bad combination.

I would suggest that you look at planting a woodland mixture (rather than grass) and you open up the canopy.

Where you live is a factor on what type of seed you should plant.