Tile Baseboards around Vanity
I do not think you will find any more of an elegant way to do what you want to accomplish. You need to go under the vanity and so something has to go there. You could try to wood face that portion - but I think you will have a less than attractive end result. 

If you were using wood flooring tile as your base boards - you might be able to make it blend. 
Either way though I think you do not have many options, and will probably end up with the L. If you notch it right I think you will find it to not be as bad as you might think.  I would silicone the back edge of the tile at the vanity edge rather than mastic at that end - so the silicone caulking can bleed through from the back side - kind of hide the sealant if you will - and provide a more seamless contact point.