RAW I think you could get it to work if you also take 3 levels of Adept and take the warrior monk tradition.
At that level you gain the Lost Tradition feature, which states " Choose a combat tradition you are not proficient in. You become proficient in that tradition. When you use a combat maneuver that requires a weapon with a particular property (such as finesse or heavy), your unarmed strikes count as having that property"
So if you use a maneuver that requires a heavy or two handed weapon, your unarmed attacks count as having that property, which would also trigger all furious critical synergies