I don’t have experience working with MSD plates in particular, but I’ve used both Biotek (now Agilent) and Tecan Hydrospeed plate washers, and I’ve had good success removing volume completely without scratching the bottom working with ELISA workflows.
At least with both of these protocols, you can have multiple aspirations happen in a single wash protocol, where you tell it to aspirate at different parts of the well. You can have it aspirate most of the volume at the center of the well (at a safe position above the bottom of the working electrode), and then move to the side of the well to pick up the ring of liquid that is usually still there. You can repeat these side aspirations until there is no liquid remaining in the well. You can try to find the lowest safe z height of counter electrode and Dielectric electrode and safely pipette there. It looks like MSD wants you to pipette here:
There’s also options such as the BlueCatBio BlueWasher or Cytena C.Wash which evacuate liquid via centrifugal force. This is probably the closest way of automating flicking the plates manually. I don’t have experience with their use to be fair, so I can’t speak to how well they work. I do know that these are generally more expensive than a standard plate washer. This Link has multiple people discussing their general experience with plate washers.
Hope this helps!