You don't want to go specifically elite hunting, instead you want to go density hunting.
The wizards biggest tool is area damage and you want to capatalize on it.
Be aware that it is insanely hard to get all the skill timings correct with this build, and this may be the single biggest cause for the difference in GR levels. In my opinion it is the hardest bulid to play properly, and skill plays a very large part.
The best way to do this is to seek out and form large groups of monsters, because a big white pack is more beneficial than wasting time on an elite with no white mobs (and no Oculus for your wizzard to stand in). Once you do find an elite don't fight it right away, instead the monk should pull it along a little bit (using cyclone) and round up an even bigger group of mobs (wizard can help here as well), ideally two elite packs and a bunch of trash so you can wipe the screen with all that area damage.
Dont stay to fight:
If you take down all the white mobs but dont kill the elite, then consider pulling it along (It will follow you a bit, and the monk can use cyclone) while you find more white mobs to form another big group.
It is also very important for the wizard to stands in the Oculus circle (Provided by the monk) whenever possible, and that the monk pulls the mobs on top of the wizzard so that Audacity will work correctly, and strongarms will be triggered.
What gems is the wizard using? Bane of the Trapped is manditory, and Taeguk is follows closely. If you struggle to kill the rift guradian then use Bane of the Stricken as your third gem.
Make sure that the wizard has elemental damage on their amulet and wrists. Elemental damage is a massive buff, and is a multiplier to sheet damage.
Is the wizard using the same build as the leaderboards? If so then be aware that it is insanely hard to get all the skill timings correct, and this may be the single biggest cause for the difference in GR levels. There is a very small damage window that is crucial, so many of the wizards on the leaderboards have insane keyboard skills, or are using third party software to macro the skills so that everything is timed correctly. If the wizard is unaware of how to time the skills or are not nimble on the keyboard then consider swapping to a more user friendly varient (Starpact or Tal Rasha).
Is the wizard struggling to stay alive? If so then that has a massive effect on damage output because they are too busy trying to stay alive. Consider spending some time maxing the Monks globe bonus on all pieces of gear that have the stat (Ancient items give far greater healing bonus), and also maxing attack speed.
Advertise for groups:
It can take a while to get the combo working, maybe try paring with other monks and wizards to see what they do differently. And then come back and try what you learned.
Last note: As @Dpeif mentioned, 3.1mil is not a lot for a wizard at this level of GR, and especially not in a two man group with a support monk/barb.