I have the same setup as you. I originally got 6.5 gal carboys because I figured if I ever have brews that i add stuff to, then I have room (such as fruits).
I have never had an issue with this. I get that issue of oxidation, but remember that the amount of beer TOUCHING the headspace is very little in comparison to the total amount of liquid. One big issue would be if you splash it too much around after its in there but the same issue could be said even for a 5gal unless it's filled to the very top.
The CO2 blanket is a good idea to ease your mind. If you don't want to invest in kegging yet (which would be one excuse to) then just get yourself a CO2 injector that uses those small bullet cartridges and that's it. Cheers.