Try to resolve the issue in a wrong way
In a nutshell, let's add overpowered blocking and parrying so the first attacker is likely to lose.
I do believe that you're trying fix combat in a wrong way Dark And Darker Gold.
The best solution is to each class to have higher HP. Barb shouldn't be able to have more than 25% HP as a base kit.
You can either give barbs access to a high HP armors which aren't accessible by other classes or grant them leveling to become a high HP target instead of being one right from the start.
The simple nature of combat has to be kept, that's the game enticed me at the first time. If I wanted to fight chivalry/mordhau I'd go play chilalry/mordhau . However, I am not fond of those games.
For those of you who feel bored of the combat it is not suitable for you. I'm not bored for example. However, I do agree that barb in melee usually outperforms other classes. In fact, I have suggested a solution for this in the previous post Dark And Darker Gold for sale.
There where some other bits and bobs these to let you tamper with an attack in advance to put in a parry early, or you colud try striking back and forth with a volley. I'm with you in a small degree that your HP is pretty low . However, starting first can allow you to play the possibility of a parry.