How do I make mayonnaise split?
Mayo that splits is typically from one of two things:


Insufficient water
Insufficient mixing leading to large droplets


(It's hardly ever insufficient emulsifier, as one yolk can do many cups of mayo.)

The lack of mixing can happen fairly easily with a whisk, but it won't happen if you're using a food processor, blender, or immersion blender.

You're probably normally making mayo that is on the border of insufficient water, so it's fairly easy to get it to break. When you added more water, the emulsion actually became more stable.

That explains why you can't get it to break, I have a few suggestions on how to fix:


Freeze it. It should break upon thawing. 
If hand-mixed, use an immersion blender on it. That should thicken a little, by better mixing. (Assuming you're not using extra virgin olive oil, which should not be blended) 
I'm sure there are some thickeners that could be added, but I've never tried thickening mayo like this. 


Keep in mind that some flavors are fat soluble, some are water soluble, so if you discard part of the water, you may be changing the flavor balance.