Burst is a major problem. PvP gear only makes it worse.
Contrary to popular belief, more PvP gear does not address the burst issue. In fact, it exacerbates it further due to there being more PvP power on gear than PvP resilience. As such, a full PvP geared player will do more damage to another fully PvP geared player than they would without any PvP gear at all. In fact, as it is right now the difference between a fresh PvP player and someone decked out is more massive than ever before.
Thus, I propose that with the advent of baseline PvP resilience, we should consider telling Blizzard to remove PvP stats from PvP gear.
To address ilvl issues, I'd say that random battlegrounds should necessitate a slightly greater grind and provide LFR quality loot. Malevolent gladiator gear should be about equal to normal mode gear but I'd say should be gated behind ratings once again; nothing substantial, just something like a min 1600 requirement for a pvp weapon (recall it used to be 1800). Elite gear should once again provide greater stats equivalent to heroic raid gear. The gating involved in PvP already ensures that high ranked players will not get their gear before heroic raiders; this will just make sure that the vice versa is true as well.
I also think ilvl squish should have happened because the difference between a full dreadful geared player with a 463 weapon against a full malevolent geared player with any slight non-pvp weapon upgrade is huge. But that's a different topic.
Good point treelife. I think removal of PvP power would fix this though (if hasn't stopped effecting healing already that is). Heals all around do need a nerf on top of the removal of PvP power though. That's an issue that wouldn't really be effected positively nor negatively with my proposed change.