Yes, you can eliminate headspace air, you just need to right tools. A Vacuvin pump can't do it as it is not strong enough and the rubber stopper leaks.
But if you use a good electric vacuum pump that can pull ~20" Hg and have a tight seal on everything so it doesn't leak back in after you pump out the headspace you have no worries about oxidation anymore.
Mike, I know 20" is near perfect vacuum where you live, but for the rest of us, that would only remove about 2/3 of the oxygen. Why don't you think the remaining 1/3 of oxygen is problematic?