Why does Mars' experience an 'ice age' at high axis obliquity, when Earth experiences an ice age at low axis obliquity
If I understood it correctly, the important point is the temperature difference between mars and earth. On earth increasing obliquity, as you wrote, leads to increased melting of ice, ie. you increase the amount of liquid water on earth.

On mars average temperatures even during summer are too low to allow for liquid water. Higher obliquity doesn't really lead to a melting of ice. It mainly increases sublimation thereby increasing the water content of the atmosphere also on lower latitudes. The water vapour freezes out and leads to ice shields extended to lower latitudes.

So in short, since temperatures on mars are too low to allow for liquid water, the extend of the ice cover is larger, when the ice receives increased insolation. 
Whereas on earth the ice cover is larger when insolation is low, since it gains mass from the pool of liquid water.