Love the idea, but the concept is flawed though.
This is just my opinion on the matter, nothing else, don't take it as otherwise, but...
What i think that "pyramid head" should be is a boss. Much like the patriarch, but instead of spawning on wave 11, it could spawn on the end of wave 10, before the patriarch (or something like it) in conjuntion with a low to moderate ammount of regular zeds.
IMO, the specimen should not be invincible though, that would be too much. It should have a high ammount of resistances (preventing exploits, like you suggested, loved the idea), and a moderate attack damage and slow move speed.
HOWEVER, he had a rage bar. If players kept too far away from him, the bar would rise. If it reaches maximum, pyramid head would then charge at the players (faster than a fleshpound), dealing near fatal damage (fatal in higher dificulties) to one player, and the rage bar would then reset (prevents abusive kiting).
Pyramid head would be able to reflect part of the melee damage dealth to him as armor ignoring damage (In order to bring some damned balance to berserkers)
The boss would have a weak point in it's back in which he would recieve increased damage, and melee attacks to that area would not trigger damage reflection.
He should be added as an official mut, whitelisted of course, to be easily added or removed from a server.
just my view on it.