How to create greywater system on a steep slope going down to a big creek below?

I've got a small cabin that sits on the side of a mountain. The ground is mostly rock, and I'm wanting to drain my washing machine and laundry/slop sink out the back of the house, but it would come out at the top of a steep grade, and will flow down the rocky bank into a fast moving creek about 12-15 feet wide.

I'm not sure how to stop/slow the water to keep it from draining directly into the creek below.

I've attached a couple of photos, 1 shows the slope under the back porch. you can see the whitewater of the creek in the background of this photo. The other photo is of that creek looking back up towards the house.

I'm open to any ideas that don't involve thousands of dollar project/systems

Thanks.

Dig a ditchon contour on the hill side, make it 150ft long so that it can hold all the water than you disharge in a day. That way the greywater will fill up your ditch pond vs flowing down.

Well, I don't think I could go 150 feet and remain on my property, but even if I could, digging out 150 feet of rock will not be fun, and will certainly result in me hitting at least several rocks at least a few feet in diameter. Even if I managed to do all of that, how long would such rocky soil hold or slow all this water?

Is there any other way, like using a holding tank or tanks, or maybe trying to terrace the land and filing with organic matter?

I'm really just trying to slow it down enough to allow plants to absorb the "grey" and releasing the cleaned water down to the creek.

Mmm...not much to go on here...missing info:

Distance to creek?
Slope aspect?
Perk rate?
Is all the available space under the structure?

but I'd say:

1) Use a Laundry to Landscape system to send the washer water to the uphill side of the house, up to the height of the washer, to get it further from the creek
2) Do whatever size swale + mulch thing you can manage for the rest of the water...ideally not under the structure

The ditch on contour is essentially a terrace. You can make the ditch as wide and as shallow as you want it. The is for the water to soak into the soil vs running on the surface.

If you can make a ditch on contour/terrace that is 100ft long and only 1ft wide you will have 100sqft of space to hold water.
Every square feet of space will hold .623 gallons of water per inch. So your 100sqft ditch/terrace can hold 62.3 gallons of water per inch.
If you made the ditch/terrace 4inches deep/high then it will hold 250 gallons of water.

So the question for you now is how much water do you discharge per day.

If you find out that the 1st ditch on contour cannot contain all the water you can always have it overflow to another ditch below and even then you can have another ditch on contour after that.

A ditch on contour is about 1ft wide
A swale on contour is about 10ft wide
A terrace on contour is at least 10ft wide, but the name implies that there is at least 3 of them in series and that the slope is particularly steep.