Would electrolysis work with a conductive (but waterproof) divider between anode and cathode?
A cell with two electrodes separated from each other and an aluminum divider plate in the middle is really two cells: one has an aluminum plate as a cathode, and the other cell has the same aluminum plate as the anode. 

In this situation, the solution does not directly connect the external anode and cathode; the aluminum divider separates the solution into two separate cells.

When you pass current (electrons) thru this arrangement, ions travel. Protons (or other cations) travel toward the negative electrode. In the cell attached to the external positive source, protons move away, and discharge at the aluminum. Simultaneously, protons in the adjacent cell move away from the aluminum and discharge at the stainless steel cathode. Hydroxyls (or other anions) do the reverse. 

You will need twice the cell voltage to get a high current, and hydrogen will be evolved from the external cathode (-) and the farther side of the aluminum divider plate. Oxygen will be evolved from the other side of this aluminum plate and from the external anode (+).

Now make a small change: let the aluminum divider go from the top of your case to below the water line, say, halfway down. Then ions can travel thru the solution. This is now just one cell. Hydrogen will be evolved at the (one) cathode and oxygen will be evolved at the (one) anode. Your separation of the gas phase by the aluminum divider allows hydrogen to be collected separately from the oxygen. BTW, you might as well use stainless steel for this divider, since it is used for the electrodes.

When collecting the gasses, hydrogen will be evolved at twice the rate of oxygen. If you build up pressure, the cell will respond by pushing liquid from the cathode compartment into the anode compartment to equalize the pressure. You may have to use a check valve or some kind of flow equalizer to keep liquid from spurting  out of one of the gas outlets.