I'm not complaining about my monk not being strong and I don't even know how he stacks up against other DPS really. My only issue is that groups don't tend to always want me (A monk) in a group. Coil is an example as I've been denied for coil a few times and told "melee DPS really isn't ideal for coil".

I don't run that parcers program but instead I go from what I personally see. When I run AK in a group and the other DPS is a Dragoon, the dungeon takes a lot longer. However, when the DPS is me and a Bard the dungeon is completed far quicker. This has been tested with a +1 Dragoon (I'm also relic and just obtained +1) and a non-relic Bard who still completes AK faster than the +1 Dragoon.

I think Titan HM is a bad example as the only real time that damage is essential (heart) is an easy time for both melee and ranged DPS to do damage.