ftp://ftp.ncdc.noaa.gov/pub/data/paleo/icecore/antarctica/epica_domec/edc-co2-2008.txt
It'll take a few days to address the rest of what you wrote. You correctly pointed out that the lag issue is dependent on the time-resolution of the ice cores. As the link above shows, the gas age resolution is dependent on the site and the age -- the farther back you go, obviously the longer the periods are. That doesn't mean that the timing or "lag" can't be examined at much better resolution than thousands of years, as you imply; it can be examined for the most recent glacial and interglacial transitions. The EPICA time resolution that I was speaking of was not for gas ages, it was for temperature and climate proxies. If you'd read the paper you'd have known that.
But the lag issue is a moot point. What I said was this:
"8. The supposed CO2-temperature lag has been addressed numerous times because it is a often-repeated (~ad infinitum) skeptical talking point. This point does not, in any way, negate the important role of CO2 climate forcing. I explain this with many supporting links in my profile (point #5). There are other Web sites that also address this incorrect assertion:" and "This simple statement does not refute the simple fact that a triggering cause can induce secondary effects which may have a larger aggregate influence."
Happer's point with the use of the lag timing is to attempt to refute the necessary role of atmospheric CO2 concentration as the primary paleoclimate temperature determinant. In very basic terms, the only climate driver capable of causing the glacial-interglacial temperature change (or interglacial-glacial temperature change, if you prefer) is the ~80 ppm change in atmospheric CO2 concentrations, aided secondarily by the albedo change caused by continental ice sheets. There's no other climatically realistic way to do it, and that's why Happer was wrong on this particular point.
I'm glad you finally noticed the time resolution granularity, about 1000-1500 years at the bottom. The CO2 cannot be measured at any finer resolution and contains at least 4000 years of CO2 smoothed into one measurement as I pointed out above. So there can't be any possible verification that CO2 "peaked" at this or that in the past. It is simply impossible to say anything conclusive about the peaks. Your statement about resolution is still inapplicable, it is nonsensical to express years of resolution when gases are smoothed at 1000's of years. That result is just lots of garbage data.
As for lag, the same gas diffusion problem complicates things. The temperature proxy comes from the ice itself which is roughly 4000 years younger than the CO2 along side of it. That delta varies based on climate when the ice was deposited. What Happer is saying about the lag is that the CO2 is a positive feedback from warmth and there is no indication that the warmth is anything other than predominately non-CO2 generated.