The OP asks " ... how should I go about doing this." Your property appears to be rather flat. Coupled with close neighbors, things can get sticky. Start by getting someone other than yourself to document the existing grades over all of the project area. Use an engineer, surveyor, LA, or one who has many years of experience. The result should be a contour map with spot elevations also shown. The most important thing is the location where water is crossing the tract boundary. Before starting the design, study the drainage law of your area. Law differs from state to state, but the most common applicaton is the civil law doctrine of drainage. Here I repeat what I said on another thread. Note that part in bold. A good overview can be found at: http://publicworks.co.marion.or.us/engineering/DevEng/drainagelaw.asp "The lower owner must accept water which naturally comes to his land from above, ..." In Arizona: https://www.coconino.az.gov/uploadedFiles/Public_Works/Homeowner_Guide_To_Drainage.pdf "A second drainage law is "The Civil Law Rule of Natural rainage". This rule states that a landowner has the burden of receiving onto his/her land the surface water naturally falling onto and freely flowing onto it from land above it. The rule further states that a landowner has the right to have the surface water falling upon his/her land and naturally flowing onto it to flow freely from it onto lower parcels as it would flow under natural conditions. The key words are "naturally flowing". Any modifications to the surface topography or the drainage ways that cause natural flow to enter or leave a property differently (different peak flow elevations, frequencies and flow locations) can create a liability and put you at risk regarding litigation." Or from: http://web.aces.uiuc.edu/vista/pdf_pubs/DRAINAGE98.PDF "A landowner has no right to obstruct the flow of surface water. The owner of lower land obviously has no right to build a dam, levee, or other artificial structure that will interfere with the drainage of higher land, according to the CIVIL LAW as it is applied in Illinois."

I like everything you've done. Having had just a little experience with heavy rains I understand your need for a dry creek. That was a huge undertaking and you brought in some wonderful rocks to use for it. Now you can do some very creative fun landscaping with your dry creek! I googled that subject. Maybe you can get some ideas from some of the photos. Hopefully other readers will have some more specific ideas to pass along. Again, thank you for sharing your photos of the process. Here is a link that might be useful: Landscaping man made dry creek ...

Look at the local streambeds and copy them. Unless you find local black lava streambeds, don't try to make it work in your yard unless you are going for a totally modernistic unnatural look. For a natural look, vary the size of the rocks, with some big ones anchoring the bends and interrupting the "stream", with smaller rocks. This is a good one. https://www.pinterest.com/pin/210754457531720328/ You want to avoid the drainage ditch full of gravel look.

I did something similar on my side yard because our houses drain to the street out front. We put down 2 layers of landscape fabric after getting the slope right, then decomposed granite with bull rock on the edges. Most of the granite has washed away over the last few years & we will be putting down more bull rock to replace it. It flows very well in torrential rain, but I do have to spray the area with vinegar quarterly to keep weed seeds from sprouting in there. We did not try to plant that area, but if we had more space we might have put some large potted plants thru there. I'll get a pic later today so you can see it.