Nice of you to add the addition of the netting. When I do this again I will put some shade cloth down for the very reason that you can roll it afterward and keep the stolons in contact with the soil. It was a bit of a risk undertaking something that there isn't a huge amount of information available for your average home owner, and I will definitely refine the method next time around.
What grass type do you use on your greens? I hear that Santa Ana is still quite popular for greens, but there is also some ultra dwarfs around that can handle mowing heights down near 2.5mm.