You will need 2 or 3 M6 T-Nuts per cabinet and a 5/16" drill bit to complete this project. The new pole socket may need fresh gasket tape to seal the mating surface.
Align one bolt hole on the new 3 bolt pole cup with an existing hole.
Mark the holes that line up with the new pole socket and drill the 5/16" holes at those points.
Secure T-Nut lightly into the underside of the wood. Gently tap it into place or thread it into a bolt and pull it slightly into the hole. You can also pull it into the hole using a C-clamp.
Lubricate the bolt threads and lubricate the underside of the bolt head.
Once they are partly secured then tightening the bolt will pull the T-Nut into the wood. Don't tighten the bolt without the pole cup in place as it will pull the bolt into the wood.
Slowly and carefully tighten the bolts so that it pulls the T-Nut into the wood.
Repeat with other T-Nuts.
The open holes will be covered by the pole socket and do not need to be filled.
If the aesthetics of the alignment are of concern, you can choose to drill three holes and use three T-Nuts if the alignment.