I run into this problem occasionally when using only one support infill angle. I tend to only use one (as show in the picture at the top of the thread) because they are easily removed - they can be squeezed and will shear off easily. This works great with the support pillar resolution turned the whole way down the 1mm (the minimum).
However, sometimes a single support angle will not work well if the support walls are very long. They will partially break loose from the bed and the wall will start leaning and may eventually collapse.
Using two or more support angles to create a grid is very stable and supports solid layers printed on top them very well, but unfortunately a 90 deg grid support structure is exceedingly difficult to remove.
My work-around on parts like this has been to define two support angles that are close to each other. For example -5 and +5 degrees, or 85 and 95 degrees. For parts where the first layer of solid fill on top of supports changes angle at different levels, I've had good success with 40 and 50 degree support angles.
In each case, I've sort of settled on a 1.6mm support pillar resolution. Tighter than than and they become more difficult to remove, wider and the solid fill on top of the supports has to bridge further and the surface quality gets worse.
When two support angles are used which are close to each other, they still overlap frequently enough to lock the support walls together. However, they have enough space between them that the support walls can still be easily sheared off.