So we are also allowed to discharge our rainwater into a surface water body. No problem. A short email to the person responsible for wastewater in our municipality and an hour later the approval.
How about an artificial stream with a natural stone bed?
That was my first thought as well. However, to be able to enjoy the stream in action while sitting in the garden, you would have to order a local rain shower for the roof every time. Sitting outside in the rain and watching the stream somehow isn't really fun.
Had thought about that too. Maybe you can even do it yourself with a pump and pond liner. I just don't know if the plants will survive it if a tsunami runs through every time it rains.
I wouldn't pump from the creek. You could make a pond at the lower end with an overflow to the creek and then pump from the pond, but that surely also costs quite a bit of electricity...