Re: head space filled with carbon dioxide.
With a full keg, most of us just burp the keg a few times, that is, put a few bars of gas pressure in the keg, turn off the gas, release the pressure with the safety valve ( or just depress the centre of the gas post if your kegs are missing the safety valve) then regas. Do this a few times and most of the oxygen will be purged out.
With a half full keg, you would need to burp a few times more.
To completely remove oxygen from a keg, fill the keg with sanitiser, and push this out with carbon dioxide, and your keg will be full of carbon dioxide.
I do not know how oxygen affects the cola and spirits mix, but I would assume that it would beaffected by oxidization in a negative way.
As to producing spirits without a still, you can try the ice way, make up some sort of wash, freeze it and remove the ice. If you use one of the turbo yeast style packs, the result will not be very nice as many of the unwanted by products that are usually left behind when distilling will also be concentrated in your end product. The ethanol shouldn't freeze in a domestic freezer, and any ice that forms is water. Or, you can muck around with some sort of solar still, and collect whatever evaporates and recondenses. Have a look at
http://www.homedistiller.org for ideas.
