I asked the pruning community for a good wisteria book for identifying the wisteria in the park and was recommended Peter Valder's Wisterias, A Comprehensive Guide.
However, once I posted a photo, two people knew exactly what it was: 'Black Dragon'!
It is the only double flowered wisteria, from what I understand, so there is no need to key it out.
Some interesting connections with the park is that W.B. Clarke was the west coast distributor of this Japanese wisteria. W.B. Clarke was, apparently, an employee of the California Nursery who opened his own nursery in San Jose. The CNCo sold W.B. Clarke's low-chill lilacs, so the Dragon might be in the CNCo catalog as well. I will check.