Try adding acid to water and see what happens.

Sure, safety aspects aside (although at a guess you'd only need to add a few drops of conc H2SO4), are there any functional/operational problems in doing this that would affect the battery performance?

Yes, the explosion.

How will you ensure the elctrolyte mixes? You can't stir it and there's no convection because there's no temperature gradient. The nearest you get may be due to bubbling as the cell reaches full charge, but in the mean time the upper area of the cell will be damaged by the concentrated acid.

civilperson,

Your point is valid but you have it the wrong way around: adding acid to water is safe, at least from the explosion point of view. Adding water to acid results in the effect you describe.
  

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If we learn from our mistakes I'm getting a great education!
 

That little amount of conc H2SO4 would rapidly mix uniformly throughout the electrolyte just on the basis of the concentration differences/gradient. That's a basic 2nd law of thermodynamics principle, a uniform concentration is lower order than two difference concentrations. Hence you wouldn't need any physical agitation like stirring to mix it up although admittedly that would speed things up. I doubt conc H2SO4 would damage the upper layer of the plates for the brief time it's there.

Anyway enough theory, I'll have to do an experiment and see if I get any improvement in capacity.  

Learned something there about mixing acids with water. Thanks. Let us know how the experiement goes.
  

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If we learn from our mistakes I'm getting a great education!