I'll just go over the basics here, but each time you were unable to out-agro my healing was when I enabled my spam-the-marked-person mode. Roughly, here's what I was doing..

1. /cast riptide [target=markedPerson] - instant 2k heal w/ 1k/tic hot, buffs next spells
2. /cast lesser healing wave [target=markedPerson] - fast heal with ~60% crit chance, equating out to ~10k to 11k heals at 1.2 casting time.
3. /cast lesser healing wave [target=markedPerson] - again @ ~60% crit
4. /cast riptide [target=tank] - recast to restore the crit buff and drop another hot
5. /cast lesser healing wave [target=tank] - again @ ~60% crit
6. /cast lesser healing wave [target=tank] - again @ ~60% crit

total casting time: ~9-12 seconds, give or take lag
total healing: presuming 3 crits = ~45k-50k

The last fight I was nearly 5k hps.. And I have no threat reduction as most tanks have no problems holding threat, which doesn't help when you're trying to out agro me..