... that the DO (and, therefore Ishamael) need the Dragon to create the necessary chaotic conditions in the Pattern that would enable the DO to fully escape his prison. Therefore, they need him alive.

The simplest way would be if the Shadow could turn the Dragon to their cause - then the Dragon could work deliberately to create those necessary conditions. That's what Ishamael was trying to do in the first 3 books. However, that method has never worked in the past (despite what Ishamael said otherwise - RJ said as much at DragonCon '05), and this time it lead to Ishamael's death.

The harder way is for the Shadow to allow the Dragon to live long enough to create the necessary chaotic conditions inadvertantly, and then kill him if he still refuses to turn when the conditions are met. That explains why the DO ordered Demandred to "let the Lord of Chaos rule" at the beginning of LoC, and why there has been a standing "do not kill Rand" order since then.

The only time that order was suspended was when the Shadow was trying to prevent Rand from cleansing saidin (presumably, the cleansing of saidin would have been more damaging to the Shadow's cause than killing Rand would have been, at that point), but the order was immediately reinstated after Rand cleansed saidin, because it was still better for the Shadow for Rand to be alive and generating chaos than dead.

Yes, Ishamael tried to kill Rand a couple of times in the first 3 books, but the thinking there is that he was so angry with Rand that he lost sight of the BIG PICTURE, and let his emotions dictate his actions.

Ishamael may also have had (and may still have) his own ideas on how the Shadow could succeed without a living Dragon - remember, he can't possibly know exactly what will work and what won't, in terms of freeing the DO completely, since it has never happened before. Backup plans, say, if the Dragon were to die.