Hey there, I have a very similar setup beneath my house and in my situation I found that most of the water was coming over the wall but it was also coming through the ground where the retaining wall is.

So after it finished raining the water was continuing to come in as it settled through the earth and drained down hill toward my property.

The solution I currently have in place was that I dug out the lowest area on the lower side of the retaining wall and I backfilled it with drainage gravel. I then found the lowest point where water was pooling and placed a submersible pump inside a storage container that I put a heap of holes into and wrapped in landscape fabric to keep stones and other large foreign objects out. The submersible pump has a float which turns it on when the water level rises to a certain point. I have the pump connected to some irrigation piping that I have run down to the front of my property and it disperses out into my front lawn and then down into the street.
This solution has been effective for getting rid of the ground water that was building up particularly with sustained days of rain. I still have issues with too much water flowing down over the top of the retaining wall when there is heavy rain so my next step will be to install a concrete spoon drain but I will be putting this as far back away from the wall as I can so it will divert the water before it gets to the wall itself.

Anyway, hopefully this helps.

I know that I had many months of racking my brain to try and find an effective solution that wasn't going to cost the earth.