Hiya Paul,
I'm really new here, kinda bouncing around checking out this amazing resource, and I spied your query. Couldn't help but run a quick search to see what other Aussies were saying about it, as I've had a few Aussie traveling buddies tell me Jack Riley wasn't the man from Snowy River at all. Jack Riley lived on a completely different river, the Murray River.
Evidently, it was a fella by the name of Francis Michin. I don't remember much about the story, or why my buddies insisted this was on whom the story was based, but I did manage to find a 3-year-old youtube video that sought to answer the very question. Was Jack Riley really the guy?
Just a little into the video, I noticed a lengthy comment. That's what you oughta read if you want to get the local perspective on who the Man from Snowy River was, and why anybody might write about him.
As for Jack Riley, he lived alone out on the Murray River. I'm betting he walked away from his family (whatever there was of it) as clean as I did when I was young. You live alone long enough, you forget, and back then, especially in Australia, it was easy to disappear without a trace, leaving not a single family connection behind. Hell, his name may not even be Jack, or Riley.
I wish you luck, but that's not a task I'd wish on the most annoying genealogy nerd on the planet. An exercise in futility, however an interesting task it might turn out to be. Maybe research Francis Michin instead. He still has grandkids alive today working that land.
Hope this was somewhat entertaining for you, but also helpful. Oh, and here's the URL for the video with the history lesson in the comments: https://www.youtube.com/watch?v=-JuUtjoHR4w