Defeat all enemies: Defeat all enemies is one of the longer floors. Varying on floor size and quantity of enemies, it can be a pain in the ***. On floors like this, the DDs paired into twos and called a direction (Three directions max from rune typically. DD set A calls East, DD set B calls West, and say Dead End (DE) when they reach the end of their path. The first set to complete their direction should double back and get the third route if applicable, or catch up with the other pair.) The DDs should pair up based on survivability, e.g. Apocalypse DRK was paired with a MNK, where the two WARs paired with each other and the SCH followed the WARs. If you use WARs, they should have PDT (All DDs should have PDT sets actually, and learn when training is a benefit, but also a negative) sets and Fell Cleave if able (meaning, be smart. Know your enemies and know your capabilities. If you die, its a hard penalty on your team). It can wipe out a room quickly. DD pairs should split up at intersections and be perceptive of how the split works (Two dead-ends, one dead-end and a continuous path, two rooms full of mobs, etc.), and make calls dependent on the circumstances. Voice chat helps, but players that know each other well can communicate concisely.
Specific enemy: Smart tabbing and intuition are your best friend here. Not much else to say. DD sets are redundant, don't use them.
Family: DD sets are best here. Family is either 3, 5, or 7 to my knowledge, so count off how many you kill.
Boss: Same as specific enemy. Split up, but come together to clear the NM.
Same time: Same time lamps should be hit immediately as you find them (Within reason. There's about a 20~30 second window between the first and last lamp where lamps can be activated and the rune cleared). That way, if you find them all in rapid succession, you clear the floor fastest. Being observant of your surroundings, and hitting multiple lamps within your radius is your best bet, leaving the others to scour for other lamps. Your team all has to be on the same page, and understand the basics here. This seems silly to say, but I can't tell you how many runs I did with a pick-up and he just mashed a single lamp for five minutes, totally killing a run, because he didn't grasp the core concept. Lamps are what kill runs.
Order: Hit each lamp as you find it, and make sure someone is dedicated lamp caller. The reason you hit on-find (and label numerically) is that once they all activate, it tells you how many lamps there are. If they all don't turn on, you're obviously missing a lamp. Faster you know you have all the lamps, the better. It also lets you execute one combination, and work from there. The callers mastery of the patterns, and your communication skills are key here. Create a simple call out for a lamp staying on or turning off, whether it be X for off and O for on, or whatever. This can waste a lot of time if people don't do their duty of calling out, or remembering their lamps' numbers. A single person holding multiple close lamps here is also viable.
Code: Sounds like you've got code down just fine. Hermes drinks are *** great for these.
Do you leave one player at the rune always? Run time wastes a lot of time.