All's well and good, until you get to adding angles together, unless you visualize A,B,C existing on a sphere and the angles between them being from the center of the sphere- are the possible angles of the sphere identical to the inverse cosines of the possible correlations? (If A and B are .707 correlated, and B and C are .707 correlated, are A and C necessarily somewhere between 0 and 1 correlated?)

Yes. If you have n random variables, you can restrict to the subspace spanned by them (or their equivalence classes). For instance, if we have 3 random variables whose equivalence classes are linearly independent, then the span of these equivalence classes will be a 3-dimensional real inner product space, which will then necessarily be isomorphic to R^3 with the dot product.

Actually, it occurs to me that I've never actually sat down and checked that angle addition obeys the triangle inequality in 3 dimensions -- I suppose if nothing else it can be done by lots of inequality grinding -- but that's not relevant. The point is, it does hold in dimension 3, and hence by the argument above, it holds regardless of dimension, finite or infinite.