The first idea is pretty much what Pseudo-Random Distribution is, and is a pretty cool way to make the RNG more consistent (in my opinion).

For a bit clearer example on this:
Let's say something, like an Obsidian Carbine inflicting poison, has a 20% chance of happening every time it hits.
However, with PRD, the actual percentage (constant) is about 5.57% chance of happening.

But Mako, that's lower than 20%, wouldn't it take more rolls of the dice for it to happen?

No, actually. Because with how PRD works, the chance of the event happening works out to be around 20%.

If the 5.57% chance doesn't successfully roll, the chance is then added on top of itself again, resulting in 11.14% for the next roll.
If the 11.14% chance doesn't successfully roll, the chance is added again, resulting in 16.71% for the next roll.
This addition continues to happen until it successfully rolls, which will reset the chance back down to the initial constant, 5.57%
This means at some point, if it hasn't rolled successfully in 16 rolls, the chance will actually be over 100% (100.26% actually)! Guaranteeing that the next roll will have the Obsidian Carbine inflict poison.

But Mako, how does that work out to be 20%?

Over a moderate amount of time, the probabilities average out to about 20%. Someone created and ran a program to test these constants out, and they worked out to be about certain constants for certain percentages. Googling will bring up a few forums about this (most notably DotA threads).

Excuse my ramblings about this, thought it was a relevant time to bring that up.
Except I'm talking about game mechanics and not lore.

TL;DR : Dracora's first suggestion will make hunting Black Kats far more consistent and a bit less luck dependent.

Trying to get 200 tokens for one 5-Star hat is pretty demoralizing when Black Kats spawn infrequently and only grant 3 tokens each kill. And from what the wiki says, Tier 1 and 2 Black Kats only drop 1! +1

Encouraging party play is also great, especially with all of the other ideas, if they were to be implemented. +1

It's always nice to have some lore to the games. Heck, the lore about Vanaduke and Almire on the wiki page is somewhat intriguing. +1