Could you attach the photos instead of having them as a download, they take a minute each to download.
From -
https://www.quailsprings.org/how-to-drought-proof-your-home/
" Net and Pan Systems
On steep hills of more than twenty degrees slope, another earthworks approach will be better suited. Called “Net-and-Pan” This earthworks system funnels rain and directs it to each fruit tree basin. Upslope from each hillside fruit tree, we create a diagonal one foot by one foot french drain. Two of these French Drains direct rain water into the fruit tree basin. This now widens catchment area to perhaps ten feet that now directs to the
trees. This creates more water harvest to upslope crops, while allowing less to streak downslope and cause erosion. By staggering these Net-and-Pan systems downslope, all parts of the hill can become catchments and directed into these basins."
I think this is the best system for your case, and I have seen and used many.
Could you install a large tall tank on the pavement filled from the new gutter and pump water to the top of the slope for dispersal within the drain system?