what i've done recently on a toon stricktly levelled with invasions:
-installed the addon to see rares selected the one who drop useful gear for me and killed them, this will boost ilvl near 800
-installed wq group finder, done invasion and wq who drop spare gear and relics (even pvp quest)
-gone directly for BS opening scenario, that was the most brutal part the second segment (the ship) is really a pain in the rear but it's necessary because you just need a quest after to unlock AK 26 and boost the artifact
-used group finder to farm shard from random bosses till 850
after that i was near 850 much depending on luck for invasions timer and wq reward