No significant grass will grow in shade that heavy, unfortunately.

OP there are some other groundcovers you could try, but I see a few things that are issues/questions:

1-you have a dag.  A big dag.  Big dags make it hard to establish new plants on the ground.  Big dags are worth the trouble though.  

All that said...are you open to other types of planted groundcover?

2-What is the primary purpose of this area?  Play for kids?  Spot for dogs?  Stuff gets parked there?  Sit out there around a firepit?

3-How much of a slope do you have?  It doesn't look like much but camera can fool the eye.

Can you find your viewing history and tell me the title of the TOH episode?

ETA:   I feel like you would get more use and enjoyment out of that part of your property if you set it up for particular uses...like outdoor rooms.  Maybe there is an area of mulch or landscape rock around the tree and deck/porch structure, with a paver path out to the rest of the lawn, and then whatever you say you want to use it for, design for that.     Don't get me wrong.  I'm not talking something hoity toity.   A plan will help you know what the best options are for a surface, whether that's a very low terrace (depending on how sloped it really is, or some kind of geofabric to hold stuff in place,  and maybe even some actual hardscape, like a paver patio, and another area that has something like pachysandra or Vinca minor that will hold a slope.  Maybe NONE of these things.  Maybe something different entirely.    I'm just throwing stuff out.  I don't know until I understand fully what it's like and what you want to use it for. Also what you are capable of doing yourself.  Looks like a rural property. Is there a tractor involved?

I love moss.  But that dog will destroy it in about 2.5 seconds.