The radius for stabilizers is actually pretty huge, 12 blocks away from the matrix on the xz coordinates. (I found a good visual guide here)
Like Wagon said, you can place crystal clusters on the underside of the platform, and also you can place four skulls on the matrix itself.
In past version it was also checking Nitor and Nodes for symmetry. This is not the case anymore, so you can build the charging station now close to the altar.
And as you mentioned already, it also checks three layers beneath the altar. I just filled a 7x7 area under the altar with clusters (not sure if it is necessary, but I also kept the colors symmetrical) and haven't had a single instability yet.