The Problem
If you're playing Denmark, you're going to war, and you're liable to pick Authority for that reason. The Jelling Stones

/

on kill benefit harmonizes entirely too well with Authority. Frequently when I'm at war, I'll overflow the right hand side of my screen with notifications that
- I got
/
/
from a kill
- The
expanded my borders
- My border expansion gave me
/
- That
gave me 
- That
gave me moar 
It's an incredibly powerful virtuous cycle, and there aren't any weaknesses. Playing as Denmark, I am easily locking up #1 in every single yield and demographic category (with the possible exceptions of military and approval) while
simultaneously conquering the world. The only yield that I'm not getting from conquest is

, and I could've even set that up with a different Pantheon if I'd wanted (I generally go God-King, because God-King). Ultimately I have more

than I know what to do with anyhow, because my population and city counts are enormous, and I'm systematically exterminating other religions.
Part of what feels so wrong about this is that killing an enemy unit is a benefit in and of itself. The victory is already a victory. When it's larded with

,

,

--and, indirectly,

and

--it becomes too powerful as a mechanism for the rich to get richer. Yes, you have to wage successful wars to take advantage of this virtuous cycle, but if you manage it, the game is over before the Renaissance. I keep meeting the transoceanic Civs and feeling let down when I realize that I already devoured my most worthy opponents.
Also, not for nothing, but the Embarkation bonus is amazing. That alone is one of the most powerful combat UAs in the game, what with the CBP's additional Embarked movement. There's only so much you can do when a flotilla of Trebuchets and Berserkers starts its turn off your coast with 7/7 moves, and doesn't stop after landing. Especially if you're a naive AI player.
Solutions
I'm focused on the Jelling Stones here, but part of Denmark's problem is that it has an incredible conquest UA, an incredible conquest UB, and an incredible conquest UU. The Jelling Stones are just the most egregious to me because of their synergy with Authority, and probably because they're totally novel to the CBP. I think you have to fix them to get Denmark balanced right.
I had thought that removing the

from Jelling Stones would be enough to fix Denmark, but Authority's synergy with the

is incredibly strong too. My recommendation would be to cut them both. I'm not sure you can add that sort of yield on kill UB/UA on top of Authority without it becoming both OP and necessary (e.g., not really a choice--you
have to take Authority, build Jelling Stones, and war aggressively in order to even approach your potential).
What about awarding GP points for kills? That keeps the heroic, skaldic flavor of the Jelling Stones without directly adding to the Authority feedback loop.
Another option might be that kills add

to cities producing units? It's less powerful as a Win Moar because if you're winning battles, then you might not need to produce more units. It makes Denmark more one-dimensional, and less of a skyscraping, universal superpower fueled by blood and thunder.
This could be super esoteric and difficult/impossible to do, but what if kills added to the experience of
future units? Kind of the same idea as Assyria having XP bonuses, or JFD's Prussia. The notion here is that you're banking XP for future units (maybe it goes into a pool expended upon the creation of your next unit?), or creating a martial culture that forever produces craftier warriors.
Or Jelling Stones could be removed altogether and replaced with something else. I really like the idea of something related to early transoceanic exploration/colonization, but there's a major risk of stepping on Spain and Polynesia's toes.