How to extract oxygen from grow chamber
Absolutely, this is actually looking more as an engineering problem rather than a biology one.
In any case, I think I have found a satisfactory answer on a paper from the 1997 Proceedings of the Sixth European Symposium on Space Environmental Control Systems. The article is called: Oxygen Scrubbing and Sensing in Plant Growth Chambers using Solid Oxide Electrolyzers.
Basically, a disk of non-porous yttria stabilised zirconia (YSZ) is sandwiched between platinum electrodes and inserted in the chamber half-way, with the other half enclosed in whatever will store the extracted oxygen. The electrodes must be porous to allow gas diffusion. The only problem is, that sort of electrolysis cell needs to be maintained at an elevated temperature (800 to 1000 Celsius) in order to work.
By means of electrocatalysis and thermal dissociation the oxygen molecule dissociates to form two oxygen atoms, these in turn pick up two electrons from the cathode and become ions. The ion is then transported by the electrolyte (YSZ) by means of electron vacancies located in the crystal lattice (basically a similar process to that of a N-doped semiconductor whereby impurities create electron holes).
I think I am satisfied with the above explanation. Doable at home? No way, but it does answer the core question.