If we cannot correlate the modern CO2 measurements at Mauna Loa with the ice core samples, then we have no reference for how the 400 ppmv would stand compared to the ice core data.
Yes we do because we believe the ratio is not altered by the process of being captured in ice.
This reading could equate to a ice core reading of 600 ppmv or 200 ppmv.
It certainly could not. Again, to arrive at this conclusion, you have to provide a chemical or physical reason for the ratio of CO2 to be different in glacial ice. You are essentially suggesting that if we captured some air in ice today, some CO2 would disappear or appear while leaving all other gases unchanged somehow and it might subsequently measure 200ppm or 600ppm while Mauna Loa (and the many other locations) measure 400ppm. There is no reason to believe this and I doubt that anyone has written a paper to prove or disprove it.
Next, Etheridge's list of issues are all minor and none would give an error of 100ppm; espescially not when you consider the massive number of samples. Including potential sources of errors and possible deficiencies is a normal part of academic writing. It doesn't mean that Etheridge has serious doubts about the reliability of ice coring. If he had written a paper about which direction the sun sets, he would have also included a list of problems concerning his final conclusion of "West".
The paper you provided already states that oxygen is not stored in the same fashion as CO2 in glacial ice
It says oxygen gets dissolved in meltwater and they are referring to very small quantities here. Water can only hold about 10 ppm and the atmosphere contains 200,000 ppm. This loss of oxygen is so insignificant that they aren't even sure if it is happening. They do not say the ratio of gases captured is altered, which is my original assertion. As you know, simply boiling the sample is enough to reacquire any dissolved O2. Not to mention that loss of oxygen would actually increase the ppm of CO2 and be evidence against anthropogenic global warming. But even if bubbles disintegrate, oxygen dissolves and some gases diffuse in certain samples, there are thousands of samples for a reason. All of these sources of errors can be factored in to the precision.
Can you show me where the 1800's overlap correlation is?
Like I said, no one would write a paper trying to establish a statistical correlation. This is because much of thata data is unreliable and has huge variance while ice core data has remarkably low variance - another reason for calling it unassailable - it is the same air.