It has the potential of better energy density and efficiency compared to Li batteries but they are not rechargeable. The major problem is the corrosion of the electrode when current is not being delivered.
That is type of cell i would eventually like to replicate. I guess what I am seeing in the plot is not true battery charging. I can charge it for longer periods and get longer discharge times up to a point. I had a cell on the bench that I left overnight. The next morning even though the separator had dried some I was still able to charge it.
Although the anion has less important roles, sulphate is not the optimal anion in this experiment. You should use Cl- as the preferred anion in your experiment: just add sufficient NaCl in the solution. This will also avoid drying out the separator paper.
Al complexes with Cl and forms complexes and that causes reduced self discharge when the cell is without load.
You may also use some glycol (even glycerol may do) to further reduce evaporation and reduce self discharge. You can see 20-30% improvement in performance. Avoid permanganate as the depolariser.