A few suggestions:

I really miss being able to invite each other to take down those hungry illiterate undead. It really encouraged people to interact, and gave another function to guilds (being another pool to draw from besides friends-but guildies are friends!).

So, besides just "increasing the spawn rate," here's some ideas.

The purpose of these ideas is not to make the grind easier, or shorter, or anything like that - though that would certainly be an effect for some of these. The purpose of these ideas is to get players to appreciate the world/game of SK more, linking lore to why you press attack, in the name of honor and spiral HQ, in the name of...kats!

Idea One:

Tribal Tracking

The Black Kats are angry in general. Killing their fellow dead kitties, large or small, makes them even more mad - as if this were possible! I think maybe the BKs don't actually care (as not all undead felines support the black kats), and are using our violence as an excuse to be violent. Killing any spookats will earn you Black Marks (especially mewkats, how COULD you-killing a mewkat could guarantee the next spookat to spawn will be a BK). Black Marks would increase the odds of a Black Kat coming after you (spawning). Black Marks resets every floor/elevator/level start, so the black kat is more likely to spawn near the end really, as long as you've killed a bunch of spookats. Killing a black kat resets your black marks for that floor, if one randomly spawns earlier anyway. Each kat killed by any member of the party would mark the whole party, no matter how many members in the squad. Think of the [party of 1,2,3 or 4] as a single entity. Death of BK resets marks for the whole party, of course.

Knowing how many black marks you have: hmm. There could be a tiny icon under your HP/shield bar (similar to temporary effects) that has a tiny little Margrel going O,..,o at you. A number indicator, same size as countdown numbers on other status/boost effect icons, would be clearly visible. Each spookat your party kills will increase this Black Mark number by 1. The icon only appears if you've killed at least one spookat. Of course, this number would be the same for every party member, even if they join later...not particularly fair, but hey, many players/friends either go full 4-ppl squad or solo+invite for other things like nests and potential radiant caches anyway. By default, black kats have the same/lower chance of spawning, regardless of spookats killed - the % chance of spawn just increases if you kill the dead kitties. Like it won't be 0% BK spawn if you don't kill spookats.

% increase by each spookat? (could even be less than 1% per, really). Well, no solid input on this from me. Commenters, give a shout out. Imo, mewkat is 100% BK next spawn (if you're not at the end of the level), cause mewkats are very rare anyway. IRL, logically, this would encourage you to NOT kill the mewkat, but game-logic, it does encourage the death of the adorable, sadly.

I feel like this would get people to actually PLAY. I find myself just running through levels over and over, only fighting when I have to in certain monster-locked areas, and of course when I see that rare Black Kat. This just feels...bleh to me. Doesn't make me engage with the game. At least with marks, I can feel like I'm building up to something.

Idea Two:

Katnip Pouch trinkets could increase the odds of a black kat spawning, cause katnip. Yes. By how much %? Well, I'll let people who comment decide what's fair. Certainly, higher star would be a higher % attraction. This would give a function to these...currently collectable trinkets.

Idea Three:

Nasty Nests

Have some nests rarely show up in haunted tunnels (like creep cakes/punkin king-but a tad more rare). I swear these exist/ed, but my memory is foggy when it's this late. These could give just one token on elite, idc, I just want to stop doing spooky candlestick keeps. Or we could have nasty nests show up in the keeps as well.

Idea Four:
Have one of the kat prestige missions be a new Scarlett Fortress tileset. Kats hang out there, too! Would open up lore for like, a jelly-kat alliance. Knowledge is power! The royal Jelly is looking for ways to be immune to curse like the Ice Queen, or something. Would be a relief from the dreary black alone in the dark-ness. Wait, isn't that the point...?

Idea Five:
Increase prestige token payout a tad. Three floors of Ouch for only four pages! Not that many (granted, a BK can spawn within the mission, but that's not a guarantee, like prestige missions should be, reward-wise). Alternatively, let us do all three different kat prestige missions daily, but only give rewards for one of them, OR lower the reward to 2 pages per, daily (that would be 6 pages daily doing all three) - and take the first floor of each out. Let these be repeatable, but no rewards of any kind at the end after the first go - I just like the arena one, honestly. This would give more level variety than the two rank missions players repeat over and over.

Idea Six:
let us invite each other when we find black kats. Mrow?

Idea Seven:

page stacking. The more page tokens you have on you, the more likely a black kat is to spawn. It wants to eat those pages, even if they are already partially digested. It seeks to extract pages from your inventory...as if your inventory is your belly...it will probably feast on your perished form as well as the um...partially dissolved papers. This might cram the player market up a bit, as people would stop spending tokens as soon as they got 50, but this makes sense to me...then again, you don't really carry that stuff with you every level...just what's in your loadout. Hmm. Perhaps a new craftable trinket, called Moorcraft Book, that draws the kats near? It would put some pages back together! But it wouldn't be a very good read. A plot from this book, half a spell from that tome...haha. ( This is similar to my katnip trinket idea - #2). You would sacrifice pages...to get more pages. You gotta spend money to make money. Or something. % increase? You decide!

Idea Eight:

Supreme Tracker pet perk. This pet perk increases the % spawn chance of any and all rare monsters, if the conditions for any particular monster are right. Sniff 'em out, robot battle sprite! You have olfactory programming right?

Idea nine:

nine ideas for...nine lives for a cat. What does a spookat have left? An echo of these nine lives? Or does each loss of life drive a kat further into darkness, with the last "life" as an immortal Grimalkin? Perhaps Black Kats could come back RIGHT after you kill them...a small chance, to be sure. Such is the power they gleam from the words they eat, at least...coming back so quickly. Each time they drop fewer pages, and they won't come back after the second time...then they ooze through the clockworks into the darkness, sneering at the light, searching for their kin...the gimalkin...Forgetting their book obsession, their prowls in the light. Forgetting...for...get...forgetting all but the hunger.

Please Note: kats choose to become BKs. It's not like, a guaranteed step in the nine life reduction thing.

Trigger for return: hmm. Only in candlestick keeps (not anywhere else they can spawn-takes a lot of kitty-kat koncentration). IF they are killed in the light of a temporary candle, then they will come back when the candle goes out. Fun strategy time!

Remember, there are new players out there. Not all of them really have a grasp of what's going on, or the best strategies to use, and stuff like this can seem hard, disappointing, and drive some away. Some of them are still in school, with finals. Not all of us can grindfest like nutters (hence being up so late...me at the end of a grind. Words. zzzz). Yes, this is a repeating event...but then again... investing in items that you only use for certain events isn't horribly fun either. BUT THEN AGAIN, a lot of arcade levels, and especially prestige, are like this...

And keep in mind, the trinket increase kinda has to be low...8 trinkets for a party of 4, potentially (and consider the potential pet perks! Wowch!) Play together! Stack!

EDIT: black and white...for icon list pics...maybe have the helmet pics be frosty recolors, and the armor pics be shadow recolors? Easy visuals and unbiased representation, beyond the fact that those two are styles. Just a thought. Unique styles would have their own pics of course.