What strikes me as the most practical way of dealing with the problem of PvP weapons being "required" for raiding is to make Resilience provide a penalty to non-PvP settings.

For example, if Resil decreased damage dealt to non-player (or player-pet) targets with a high enough conversion rate, this would basically kill PvP gear for PvE uses. 1% damage reduction per 180 resil would be approximately an anti-crit rate. This wouldn't have much of an impact on healers, but the need for high ilvl weapons is mostly a dps-thing.

Of course, the major reason that this is a problem, compared to WotLK at least, is that the PvP weapons were horrendously bad in PvE. Secondary stats were significantly more valuable in WotLK, and the combination of resilience itemisation and inflated stamina lead to serious drawbacks for those using PvP weapons. For example, an ilvl 245 PvE dagger was superior to a 264 ilvl PvP one, and the highest pre-raid weapons, the ilvl 232 ones, were not much worse than the PvP ones, unlike the current situation where PvP weapons would be significantly superior to pre-raid ones.