I leveled MRD and GLA to 30 recently using only dungeons and at pretty much the exact same time. (The GLA leveled in the dungeon first, collected the gear and then that same gear passed down to MRD, so the MRD actually had it easier being overgeared).

The thing that I most noticed while doing this was that the MRD was substantially more "squishy" while using the exact same gear and running the exact same content in the exact same way (my style/tactics don't change that much between the two). To generalize the difference between the two, GLA has defense but lacks offense(threat) and MRD has more Offense but lacks Defense(block/cooldowns).

As a healer, there is only one thing you can do to help this situation.
REPOSE.
Repose is your best friend, learn it, love it, macro a /emote to tell which <t> you are putting to sleep.
Reposing a target or two will make healing a much easier job.
You will every once in a while find a tank that will not adjust their tactics to account for CC/Sleep, or even openly ridicule it. Please realize that these are extremely bad players and any poor performance is on them and not you. Players that know even the most BASIC of MMO play know how to handle CC. It's considered a core thing to know, like pulling and holding threat.