Chess variant suggestion: Oligarchy Vs Monarchy - is it balanced?

I had this inspiration for a chess variant and I feel like it might be pretty well balanced. I suppose it might need some testing or refinement, but for now I'll just share it.
Player one (the Monarchy player) has a normal set of chess pieces
Player two (the Oligarchy player) has sixteen kings, placed in a centralized position of 4 rows of 4 kings. Player two must lose all kings to lose the game, but moves two kings per turn. They must move two different kings, not the same king twice.

The idea behind it is that the Oligarchy player just needs to get one piece for free, and exchange pieces 1 for 1 besides. That will leave them with two kings - enough to corner the other king and take the king while both are protecting each other. The game becomes a sort of defense game, trying to keep all your kings protected by the same number of pieces as the opponents attack with. There are certainly ways to trick the Oligarchy player into moving a king away from the other kings it was protecting, thus winning one or more for free, but there are equally many ways to trick a Monarchy player when the Oligarchy player can move two kings. Plus, as all kings protect all adjacent squares, they are actually pretty defensive, if close-ranged.

What do you think? Any ideas, refinements or suggestions?

player one has so much going for it

I updated my post with a bit more explanation.
Are you sure the Monarchy player has it easier? Do you have any suggestions for improving it?

STILL MONARCHY HAS MORE PIECES

Oh. That was a brain fart on my part. sorry about that. 4x4. Not 3x4. I'm editing the original. thanks for pointing that out

I think the Oligarchy is much more powerful. Monarchy's extra firepower is useless because they have no targets.

ee------------------------------------

I agree

It becomes a game of each player trying to get a free piece, in a 1x1 exchange of pieces it will end as a draw every time. I believe that techniques could be found for each player to trick the other player into leaving a piece undefended, or defended by less pieces than they are attacked by, leaving the other player ahead

But since the Oligarchy can move two kings per turn it will easily be able to pick up an extra piece.

Which would mean sixteen kings, not twelve, if you're sticking to the 4x4 instead of 3x4...

all kings is usually not a good idea unless you have compelling strategy coming from other areas, because there are really no weak spots on an all kings army. also two moves a turn is quite strong. and hard to balance.

if they get 16 kings (4x4), I do not think they could lose even with one move per turn

yep. sorry. fixed now

I'm open to suggestions for balancing or fixing this game idea. I'll be honest, I got the idea in a dream, so it wasn't likely to be balanced from the start.

I suggest something other than kings, one space movers are a good idea, but maybe you should look into the Shogi generals (golds and silvers) as potential pieces. because rn, its not an issue about balance, but simply that the king's are not going to have any weaknesses or strengths making the game more boring.

I would make first draft with 8 kings and 8 pawns instead of 16 kings. If they have multiple moves and basically no checkmate threat, I think they would still have upper hand. 
Basically what you need to do is find balance of the double move and impossibility to be checkmated on one side with material advantage on other side.