Great crawl, but I concur about the fact we don’t know the FO wants to kill Luke. One solution could be to reinsert one part of the theatrical crawl :

Luke Skywalker has vanished. In his absence, the sinister FIRST ORDER has risen in secret from the ashes of the fallen Empire and will not rest until the last Jedi has been destroyed.

Or you could also change the end:

Desperate for her brother’s help, Leia has sent her most trusted pilot to Jakku, where a clue has been discovered to find Luke before the FIRST ORDER does…

Or…

Desperate for her brother’s help, Leia has sent her most trusted pilot to Jakku to retrieve a map, which could lead to find Luke before the FIRST ORDER does…