Bear in mind people like this almost always do one of two things at the start of the battle:
a) Hide in a corner for about a minute
or
b) Break from the pack and flank
So nailing them with early ranged attacks isn't generally viable. They know people are going to gun for them and they tend to avoid situations that will get them pelted with arrows.
Also bear in mind that they actually tend to excel when a bunch of scrubs surround them. They just side-swing in a frenzy while the mass of enemies TKs each other or else has a weapon raised, trying to get a clear shot, and thus isn't blocking or parrying effectively...
I think there are two or three good counters for this situation:
1) Cavalry. Lots of these ringers are not that good against horses. A popular ringer weapon like the bec is pretty mediocre as an anti-cav weapon. Granted they generally stay out of open fields for this very reason, but if you see them and you see friendly cavalry, harry them a bit to distract them but try to keep distance so the cav can run them down.
2) A couple good defensive infantry and some archers. If I have Goretooth or something on me and I know I have archers paying attention, I'll always aim to just keep myself alive, try to slip in just enough attacks to prevent him from freely wailing on my shield and arrange to be at an angle where the archers can shoot him. I'm not trying to kill him myself, I'm just trying to distract him for the archers.
3) A good attack with about 3 infantry, especially combined arms. 1 shielder + 1 longspear + 1 heavy maul is a horrifying combo and even the best of the best will be screwed against that combo. Better still if those three have some throwing weapons between them. It helps to soften up your target a little and can put them off their game. Plus, 3 is a good number -- more than that and you can get in each other's way.
So, yeah, when I'm on my shielder, I will engage these ringers and try to draw them into a fight where they get outnumbered, relying on my shield to let me live long enough. I'll try to get hits on them with my throwing axes if they turn away from me.
When I'm on my 2-hander, I steer clear of them unless they are distracted by someone else.
When I'm on my archer, I will always try to shoot them above all other targets.