The open circuit voltage of a battery: Does it decrease with increase in pH of electrolyte while the voltage across a load increase?
Your aluminum half cell has a standard OCV (i.e., at 1 M $H^+$) of 1.676 volts. Ref. 1
You don't have standard conditions, but that doesn't matter; your conditions do not change for this half cell.
The other half cell is a reduction of water, in alkaline solution, with the electrons from the aluminum to produce hydroxide ions.

The CRC Handbook confirms -0.8277 volts for this reaction. I had intended to use a picture from Ref 1 showing the OCV, but it was incorrect by a factor of 10! Just goes to show you that you can't trust it just because it's in print, or online!
The point is, this reaction wants to consume hydroxide ions and generate electrons, but you are running it in reverse by pumping aluminum electrons into it.  When you increase the pH of the half cell, you increase its voltage by giving the half cell more reactant - but then you are fighting it because it is yielding to the aluminum voltage, so your total OCV out decreases. That's why your cell output is so low (that, and the non-standard conditions). But the good thing is that the extra ionic concentration decreases the cell resistance, so it can supply more current to your 1k resistor even with the lower OCV.
Ref 1. https://chem.libretexts.org/Bookshelves/Analytical_Chemistry/Supplemental_Modules_(Analytical_Chemistry)/Electrochemistry/Voltaic_Cells/The_Cell_Potential