The IPCC showed clearly that the Medieval warming period was not as warm as today. I find it difficult to understand why you would contest that, or why you seem to think that more proxy data from sea levels would change that. Considerable proxy data (apart from the one that you homed in on) show a cooler Medieval period. Even for the Northern Hemisphere. And the reasons for the warmer Medieval period apply primarily to the Northern Hemisphere.
Regarding your point that it is not possible to make meaningful estimates of Medieval global temperature, I'd say, of course. The data the IPCC used to reach their conclusion gives relative rather than absolute temperature measures. Proxy data, as I understand it does not give an absolute measure of temperature. Tree rings show relative growth rates from year to year, for instance, so will indicate relatively warmer and cooler years, but can't be used to derive absolute measures of temperature. But what the IPCC proxy studies clearly showed, as part of the data that led them to the conclusion that the current period is warmer than the medieval, was that most proxy datasets showed cooler Medieval conditions than now, even in the NH.
And, repeating myself, other evidence also shows that "now" is unusual in that the conditions which made parts of the Medieval period warm are not repeated now and only CO2 emissions provide an explanation for warming now.
Getting more sea level proxy data will not eliminate the current proxy data that shows the Medieval period was overall cooler, nor would that alter the analysis on causes for warming then and now. So it seems to me that what you suggest is a bit of a red herring. It doesn't hurt to get more data, but it's not going to statistically overturn the weight of proxy data sets we already have.
Do you contest the IPCC's conclusion? I can't see any grounds for doing so. Seems to me that the IPCC have indeed worked through this step by step with at least ten proxy datasets giving them a view of relative temperatures and explanations for the warmth that was observed in the Medieval period.
Nothing sensational, just already enough evidence.
