The Main Idea
The core should be a massive mini-game revolving around defending an outpost surrounded by monsters in a swarm themed environment, with ever-increasing levels of difficulty, and a boss-like nature. It should pay more than Firestorm Citadel, but should be a rarer occurrence. The Spiral Knights should stay on Cradle after finding their stuff due to the potential to further mine the core.
How Would This Work?
So you're going down to the core in some arcade gate, and find a small facility with a mineral deposit box of some sort. This mineral deposit box would determine the "theme" of the core when full. Once filled to the brim with minerals, the core would open for a brief time to allow knights to go down and "mine" it. Two to three days later, the core would close.
The core would give the option for a larger party size. This would be to accommodate guilds, and allow for increased teamwork on a larger scale. So after finding the core open and talking to an NPC of some sort, there would be some option to bring all of your friends. 1-8 players, is the way I imagine it. Maybe 1-6.
After paying some amount of energy to descend into the core, either 10 or more, the knights would be tasked with defending a mining box of some sort as it gathered the energy found in the core to bring back up.
Enemies would spawn around the knights in a room! But what enemies? Well you see, the knights just put minerals into a gate box to "build the core"... so we have something to go off of, like with gate construction. Optimally, the numbers of all 5 minerals would matter in this decision, rather than just the top 2 or 3, making for more "core combinations". There are quite a few ways you could determine, based on the order of the 5 mineral types, what would happen, but why tell the player? Make them figure it out, make them keep a record and make them research it.
But people are going to be expecting a boss. So we should give them one! But it shouldn't just die and end everything, because that would be terrible. Rather, the "core boss" should take on a form based on the enemies and themes that the knights put in via their minerals, and should react like so. It should go away briefly, and then return once "defeated" and should take a while to beat down.
Which brings me to the next point- There is no time limit. Only increasing difficulty. I don't care how good you are at Spiral Knights, you're going to die at some point, and once you die a certain number of times, you're going to have to go up to Haven, or otherwise expend all of your crystal energy on revives. But the thing would be that you'd be getting paid indefinitely, or at least until you died. The balance, would lie in the fact that the enemies would continually be getting stronger. Not just "Stronger" per say, but "harder", "better" and "faster" as well- all in variations. Some would do more damage, some would be harder to kill, all would drop crowns.
This sounds tricky to balance! Not so! Run the test server, get everyone pumped- figure out the average ratio of enemies killed per life, and then model the payout after it. If the players kill 100 of X enemy before dying, and you want the average payout for that level to be 16K per the 100 energy that they spent to get down there, then each enemy should drop an average of (16,000/100)/100 crowns.
Eventually the knights all die. When this happens, there will be a very short period of time before a revive is required, perhaps a minute at most, before the knights are pulled back up to the pre-core that we have now. Then, the knights will be paid in tokens towards getting new armor from the Spiral Order, or otherwise rewarded in some way for their "Service".
You cannot "Win" against the core, but it does get progressively harder indefinitely.
Why Would This Work?
What do people want from the core?
-Some sort of boss
-Content that doesn't favor any one category of monster
-A new, greater challenge.
-A teamwork based something.
What do we want to avoid?
-Ending the story-line by having the knights fly off and return to Isora.
-Leaving no or little reason to run random levels in the arcade/missions.
This idea fulfills these things, as well as opens new avenues for content- "Opening the core causes more worlds to get pulled in!" would be a viable excuse to add random levels in, as well as "Tinkinzaar, whom is corrupted by the swarm, has access to the energy found there." In that way, it both fits and extends the story behind Spiral Knights.
/e claps
Best suggestion for the core I've seen. +infinity