The short story? I ran these legs empty. There was no question of carrying on running in the cool down walk time.
Looking at the track on the map, I ran a total of about 3.5 km before the cool down started. Of those, 2 km were during the combined warm up walk and first ten minute run. My warm ups involve a lot of loitering to lunge, try to kick my bum with my heel, can can dancing (well almost), and little jogs that go nowhere, so most of that 2 km belongs to the run, which is quite good, for me.
To start with, all went well. The warm up worked well, and so I quickly got into a nice stride along reasonably level roads or gentle downhills (with one little thing us highly experienced runners no longer call "hills" near the start). When I got onto the highway shortcut, I turned on a bit of speed to get off there as soon as possible, then it's quite a steep embankment down to the road under the highway, and after that the hills that we still call "hills" (even at this advanced level) start.
The first hill is quite steep, but I went up it quite nicely. The only problem I had was I nearly got hit by someone flying off the off ramp that comes in at the crown of the hill. I didn't notice him partly because he was going too fast, but also because my mind was preoccupied with the fact that just a little way ahead was a downhill section I was starting to either crave or look forward to (one of the two).
After the downhill past the off ramp where it's a good idea to keep a careful look-out comes the Evil Hill. It's at least as steep as a badly designed staircase, and it goes on for many imagined miles. It didn't help, outwitting it by cutting the corner at the bottom.
I tackled the Evil Hill with plenty of enthusiasm, but it countered by tackling me with even more enthusiasm. By the time the first run had expired, I was half way up the Evil Hill, I was dead, and walking just added to the tiredness in my legs. It was quite a hard recovery walk.
I was still on the Evil Hill when I had to start running again. Fortunately this was on its upper reaches, where it becomes just an ordinary "fairly steep hill", so I set off S-l-o--w----l-------yyyyy (ow!), made it over the top, and carried on slowly, knowing that up ahead was the next hill. If I chugged along in the comfortable zone, I could postpone the reckoning with the next hill.
As I said, the second run was hard. I had nothing left in me when Laura said I could walk again. I almost had not even a walk left in me. The cool down walk was up the steeper part of that next hill, and was quite a challenge, itself.
So it was Fantastic! What a great run! (once it was over). I might as well teach myself to think that, so that the next challenging run is something I'm better prepared, mentally, to Enjoy.