I ended up being left with Dragons.
For Dark types, I hunted for Rocket Grunts, and hoped for the Ghost Grunt (Sableye), Fire Grunt (Houndour) and of course, Dark Grunt (any dark types).
For Ice types, the Ice grunt spawns felt rare so I really had to diversify. Had to hope for Water (Seel), Ground (Swinub), Grass (Snover) and Ice Grunt (any ice type). Though, being able to use Glacial Lure (or position myself at someone else's Glacial Lure) certainly helped with it.