Chopping down trees that don't have a firm base is very difficult. Around here some of the soil is very rocky and on occasion you can get a tree which isn't strongly rooted. Upon impact, a lot of the energy of the blow goes into moving the tree and thus the penetration is very low just as you noted. The best bet is to use a saw to do relief cuts.
I won't chop on rotton wood of any size as it can break simply due to the vibration and have seen tops and branches crack off and come down. Just saw them down completely, and be careful as they can break off under their own weight near the top when they start to go.
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