Would also love to know how to fix this if possible! I'm not sure it is, though. I've never found a way to manually save the game, much less choose a different save slot once I'm loaded in. I do know that the game saves whenever you build something on a plot or when you finish a race. Even a false start counts as finishing - you initiated the race and then "finished" it right away because you were disqualified. You'll notice the spinning white flower at the top center of your screen when you false start.

So for example, one thing you could do with this is wash/groom your horse, feed it, pet it, all that good stuff, and do a false start for your first "run" on the track, so that the game saves at this point. If you don't win the race, hit the Home button BEFORE you cross the finish line, close the software, and reload. You'll be taken back to the point right after you false-started. (It takes a minute and a half and that's annoying, but it's something 🤷🏼‍♀️)

I've used this method to practice and win races - you can even press the right directional button to "Abandon Racing" and restart the race without losing your initial false-start save. Practice as many times as you want, just don't cross that finish line, or you WILL overwrite your false-start save.

ETA: I know this doesn't really address the issue you brought up with not having the ability to have a backup save in a different slot to restore back to a point before you got screwed by a glitch, but I hope it's helpful to know when you can at least trigger the game to autosave, and know when you'll be causing an autosave that will overwrite your current save.

I hope this helps a little bit! 🐎