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I do not have the papers in front of me so I can only provide some general comments. If you have links to them I will be happy to review and respond in detail.

Argentinian Glaciers. How a glacier grows is related to temperature and precipitation. So how did Soon correct for precipitation effects? Without knowing this it can not be used as a temperature proxy.

Chinese Cultivation. That paper actually is more concerned with how solar output changes climate (specifically as measured by oxygen isotopes and carbon isotopes). It does not appear to give actual temperatures but ties the solar record to historic climate records previously published.

Finally, regarding stalagmite composition, these are sensitive to precipitation and geological and visitation changes and thus they must be used with caution. However without the paper I can't say if the author corrected for these.

Now, I have answered your question, could you please address mine. Do you feel that Soon's methodology as presented in Soon's paper posted by WOSG is scientifically sound?

There are a number of hypotheses in the paper. The most explicit one is about measured climate anomalies correlating with LIA or MWP. As you point out, the anomaly correlation can be cooling OR dryness OR wetness in the LIA and warming OR dryness OR wetness in the MWP. But the paper also proposes hypotheses for a shift from wet to dry or from dry to wet correlating with cooling or warming. The text had some explanations for these occurances but the tables only had the occurances which could admittedly point either way. But the conclusions are separate, that the 20th century is not the warmest, nor the most climatically extreme.

In my opinion Both conclusions are supported by the data. Clearly the climatic extreme question is resolved beyond a doubt, there are far fewer in the 20th century than in the previous 11 centuries. The warming and cooling is supported less fully, but still quite generally. The difficulty of correlating the proxies to actual warming and cooling is discussed as are many possible local effects that correlate wetness or drying to cooling or warming. In many cases warmer meant wetter and cooler meant drier as explained by plausible local phenomena. There were exceptions that were also fairly well explained.

I would say the two conclusions are hard to separate because of the relationship of both types of measurements (temp and precip) to the proxies. But the implication that dryness and wetness correlates with temperature changes is well supported. And so then is the conclusion that the 20th century is not extreme in either warming or cooling. As for warming in MWP and cooling in LIA, they seem to be well supported although not as clearly as their being extremes of dryness or wetness. The proxies clearly indicate that, but not as clearly the temperature. The temperature conclusions are obvious for Europe and N. America, but less for the rest of the world. But there's little evidence for the rest of the world that the LIA was warm or that the MWP was cool anywhere.