Oxygen absorbing caps have yet to be proven in my eyes as beneficial or worth it. Wait out your fermentation. When it is complete and clear, bottle as per normal -priming sugar and you will be fine. Don't worry about the tiny bit of headspace.
Even if you prime the bottles the oxygen in the headspace won't be driven off nor will the yeast metabolize it. You'll have the same amount in the bottle either way.
Yeasts in Food by T. Boekhout and V. Robert (eds.) said:The contribution of bottle conditioning to the final quality of the beer are twofold: firstly, the carbonation of the beer (6.0 to 9.0 g of CO2/L) and, secondly the removal of traces of oxygen that have dissolved in the beer during the filling process. [...] Refermentation in bottles eliminates the negative impact of oxygen, which may have been picked up during filling, on the early staling of beer.
Antioxidant capacity of bottle-conditioned (containing live yeast) beer by N. Morris and M. A. Daeschel. said:ts well known that bottle-conditioned beer has a longer shelf life. This is likely due to the ability of yeast to metabolize any free oxygen present[...].
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