Ten golden Digletts. You can manipulate the RNG by wasting frames. I improved the last version of this TAS, uploaded a few hours ago, by catching the golden Diglett instead of the regular one at 0:45. I had the idea that once goldens start to spawn, I should only catch goldens. Even though I was pretty fed up with this project, I don't regret going back to test this idea out! I feel like I got pretty lucky because even though you get a few frames to try out to manipulate the RNG before a throw, it's not guaranteed a golden will spawn in those outcomes.
It's just a guess, but I think something around 37 could be the maximum possible score. While I only caught 22 Digletts here, I think it's ...