If you do this again, you might try experimenting with resistance welding. I think a bar-shaped electrode spanning the wires near the edge could be used to run current through them and join them to the frame, similar to what's done to make welded wire mesh (video). Connect to your welder somehow and blip the pedal.
I wonder if a spot welder would have enough juice to do that? Make up some bar electrodes that would hold a segment of wires to the frame. The screen I made up for the sprint car was 0.035" wall tubing and the screen wire is 0.040" or so, and it's all stainless. I don't think the current required would be all that high.
I bet a typical spot welder would do the job if you can dial in the current, duration, and contact pressure. I'm not sure how sensitive it would be or how strong the weld would be or if any sort of shielding or special cleaning would be needed or or or. :)
We use something like that on the brake and Radiator ducts on the Rolex Cars. For the longer races we use a plastic filter cloth similar to the 3M red abrasive sponges. Lets us rip them out at fuel stops over the long races and collect some of the smaller debris from bending up and getting embedded in the radiators.
The 911 GT3 uses 3 smaller radiators in the front and it does not take too much road debris to clog them. Having something that we can quickly take out and stuff new ones in really helps. Usually only change them out once or twice over a 24 hour period but it does help.