Honestly, the game hinges on the strength of healers now, which is why I tend to not let the Tank be the only one to pressure them.

IMO, this is where I said things like "sustained damage being important" come into play. The best I've been able to come up with at this point, and is hard to communicate is to split the healer's focus. It's easy to heal one target, it's not to try to heal multiple in this version of PvP. So threaten the healer's own health with one dps (typically the lower one) and the tank - with the tank limiting their CC. Then, when the healer makes the hard choice of who to appropriately heal, the Tank CCs the Healer, and the DPS converge their burst on whatever target the healer chose to neglect in favor of saving.

It's tricky to pull off, especially with communication as restricted as it is, but doing this tactic repeatedly makes it hard for the healer, who's already going to be strained trying to keep up with all the DPS going around. Enemy Tank and Healer cooldowns really does mean you need to be putting out consistent damage without running out of your own resources too quickly. The idea is to bait out the strong defensive and recovery cooldowns, then catch 22 them into making a poor choice.

Again, not easy to pull off at all, but it works. That's why just blindly focusing one target isn't the best tactic at all times. These things will begin to iron out and become more prevalent with time though.