So the main thing about Minstrel dps, in my opinion, is that the whole "ending" skill, the Coda, is a big waste of time. With the right legacy and traits, Anthem of War gives +5% melee/ranged and +15% tactical damage and also +6300 physical mastery and +6300 tactical mastery, for your entire fellowship (it rocks solo, but it's even better in a group). That's way too big of a boost to just throw away for a skill that basically is just another cry/call. This also lets you spend class trait points on things that matter more. Also, bubbles are usually too small to have any sort of an effect.

Traits
Red: All red traits, but I ignore the following:
The Fundamentals (boosts ballad damage), Piercing Ballads (ballad crit chance), Emboldening Finish (because I ignore coda), cacophonous echoes of battle (because echos of battle does a few hundred damage every 5 seconds -- my autoattacks do more damage than this), Improved Coda of Fury (because I ignore coda). Enduring Morale is only 3/5 because it's only a couple hundred morale.
Yellow: 5/5 Vocal Stamina (shorter anthem cooldown), 4/5 Extended Anthem (longer anthem duration), 6/6 Tactical Mastery (more tactical mastery and 5% tactical mitigation to possibly go overcap), 3/3 Shielding Cry (15% damage reflect on the entire fellowship for 23 seconds -- base skill cooldown is 10 seconds)
Blue: 5/5 Soothing Voice (higher outgoing heals, counts if cast on self), 2/5 Improved Bolster Courage (bigger BC)

Skill progression
I've timed how long it takes to get skills off and the difference between:
Ballad, Piercing Cry, Ballad, Call to Orome, Ballad vs Ballad, Ballad, Ballad
can be measured in tenths of a second. It's basically the same. So cry and call in between ballads, or Cry of the Chorus then Piercing Cry (but I tend to save Cry of the Chorus for emergencies, like if i get chainstunned and need ballads right now or know that there's a boss coming up with some space between mobs).

Then Anthem of War of course.

As soon as three ballads are up, Call of Orome to debuff the mob(s) to light damage followed by:
Cry to Fate
Call of the Wizards (longish animation time -- good time to circle strafe around/through target so mob(s) spend time turning while you get it off)
Cry of the Valar
Cry of the Second Age (requires mobs be within melee distance, so always be within melee distance of multiple mobs)

Hit minor ballad a time or two while waiting for one of the above to come off cooldown, then repeat. I would be hitting ballads a lot more if I was using coda, and increased coda damage doesn't offset decreased ballad damage (compared to a higher damage skill), plus I'd lose anthem of war. I have the "dissonant strike" traits in red, but that's only because I want the +mitigation if things get crazy. It's higher damage to not put points in that trait and to instead put 3 points into The Fundamentals and 3 points into Piercing Ballads, but I want the +mitigation.

When one mob is about to die, pull it within range of another mob, then kill the first. Try to never let yourself get out of combat so that you never lose Anthem of War.