Drainage problems in yard

Hi H1 Team!

We've got a few issues with drainage in our backyard. Back story is that we're on the side of a slope and have a number of cuts and retaining done to support the site. The retaining walls all have ag lines behind it's more the general grass areas.

What I have realized is that the issue is we have hard rock and clay earth with a small amount of soil on top then grass. When it rains a lot I believe the issue is that the soil gets soaked but it does not drain away below.

MY thoughts which is what I'm hoping can be validated or changed is:

Across the area where we have the most retained wet we dig a trench into the clay/earth; fill that will gypsum, gravel and an ag pipe 100mm then cover with some geo-fabric/matting to keep soil out of the trench, lay the soil back down and then grass. Run that line across the wet areas of the yard and connect back to storm water to the street.

Is that the kind of thing that can assist with drainage? DO you think that will help or resolve the soaking wet areas?

Cheers
MArk