There seems to be a massive advantage to be a first player in this game. You may get to the enemies from the Event deck first and claim them as reward, you may get the most profitable neutral cards, etc. And the last player have all of this as a HUGE disadvantage, because him/her may be not able to get anything useful from neutral/enemy cards at all.

Is there any rule that balances this mechanic? Because a little 'bonuses' from event instants are too small to balance this right.

I suppose that possibility to shift 'first player' counter clockwise each game turn may do the trick. What do you think?

I would say shifting clockwise would be better. Don't know why but I would.

The Event deck theoretically should be balancing out some of that. I know Resurgence of the Dragon Lords gives the non-1st player a free influence to use every turn and an extra card. I cannot remember what the other decks give. I know some of the Runes are unbalanced in Rune Wars scenario in comparison to others, namely the take 1 damage to gain an extra card (?) a turn. Drawing that usually is the game over for the other player, I've found.

You could try using a snaking turn order. It would go like this: 1-2-3-4-4-3-2-1.  I know it's a long time between turns for the first player but it might help average out the benefit of going first. Personally I like he idea of just shifting first player at the end of each round. Counter-Clockwise makes a lot of sense as the last player to go now becomes the first player. The problem with that arrangement is that the previous first player is now going second which means he is still ahead of the other two players. Maybe it all balances out, I don't know, but you'd have to play a lot of games using each method before you got a feel for the balancing effect.

What about flipping over a new event card at the end of any players turn where the event card has been defeated as opposed to flipping over a new card at the end of the entire round? How do you think this would effect the play of the game?