Rick,
Sounds like an interesting read, thanks. I like that the title includes man and nature. You take away nature and man (people) wouldn't be around long or at least want to.
When I took a look on a whim it was pure luck if in the period of hour and half I found a possible track of a cougar. To me it looked like whatever it was stepped down (rock ledge) with it's front paw, then the rear paw planted in front of it. I wanted the exercise, needed some ideas for painting, some photo ops.
From my experience with the parks its more of dusk to dawn getaway for the animals. You get semi feral turkeys during the day, squirrels. Oppossums and armadillos in the low light hours. During the day you notice a lot of rooting done by feral hogs, or javelina's.
IMO the animals don't live in the park proper, instead the less accessible edges and adjacent private back country. As for the Fredreich incident I'd imagine the animal felt its exit was blocked. Passable trails are few and if you make your living through stealth crashing down a hillside isn’t in your comfort level.
In an hour an half I worked my way up a near inpenetrable rocky hillside. With bad socks the first time, I pretty much lost the skin on the back of my heels

Long sleeved shirt was a smart choice, because you had to push, crawl, cut through the underbrush when you weren't following the game trails. The game trails are circuitous and correspond with rock ledges and paths of flooding run off.
As you approach the more open sanctuary of the top you spook the animals there whose departure sounds like boulders rolling down a hill. That first day I heard what I expect was three deer spook separately. Soon after the brush opened up to plateau of various cactus, grass, small trees, flat rock, lichen and pooled water.
Trip 1 wildlife inventory
3 deer
1 hog or javelina? Didn’t see it above the underbrush, just heard something that had to weight at least 40 pounds charge down the rocky hillside. (Droppings and large rooting areas)
Trip 2
1 deer
1 unidentified animal skulked away from my auto near dark
Trip 3
9am nothing
Trip 4
1 deer
1 armadillo
The only sign of people along the way was some cut branches probably used for surveying and an older oxidized aluminum CO2 cartridge used in air rifles. All of these far below the plateau. It was a sanctuary that not many domestic animals would bother with.
I toured this area 4 times. The first 3 times regardless of how I thought I might be covering new ground I passed 3 of the same landmarks. A decomposing red balloon that looked like blood, a pool of water captured in a rock that had a vague cat like print in the sediment and a golf ball that had practice printed on it. Bottom line there were very few passable trails in or out.
Not far from civilization yet highly compartmentalized nonetheless. Close enough that a house placed on a overlook could drive golf balls to the area.
I bought my house in the area because my research showed that the city had purchased much of the area for conservation purposes. It also backs up to 1,500 undeveloped acres.
However, in the period of a year and half three major hilltops have been leveled and developed for high end communities. This area has one of the highest densities of deer per acre in the state. Population control is mostly by automobile. However, there are packs of coyotes which work the edges of the 1500 acres. Cleanup is handled by a squadron of buzzards you can see on a private cellular tower erected by a doctor on Scenic Loop road.
I don’t doubt the rain has displaced a number of animals. My grandmother used to talk about all manner of creatures which would be found on higher ground in Rockport after hurricanes. The riverbeds that I would scout for cretaceous fossils are mostly likely difficult to navigate. They have a few small overhangs and minor caverns.
I fish a lot, used to hunt almost continuously as a kid growing up in Helotes. One thing I know is the more game encounters humans or human sign the more likely they will avoid that area for a time.
When I fish, I fish the areas adjacent to popular areas. I used to fish a jetty on Cape Cod the first part of Jetty you could see fish but you couldn’t catch them. I waded across a broken section and like magic your arms would get weary from catching the educated fish.
When I added a second motion activated light on my property the deer found other areas for sanctuary. I still get deer on my flat roof from time to time. My house is cut into a hillside. I’ve walked around and met them. You can also hear their distinctive walk. They take a step pause and listen. Why walk on the roof. It's a nice view : )
So based on the terrain, the nature of mountain lions, I find it unlikely that any definitive sign will be found by biking and hikingaround the public trails on the parks. There are still a number of semi contiguous areas that a mountain lion could range.
As for statistics see the attached document. Statistics are bookmarked.
http://tchester.org/sgm/lists/lion_attacks.html