Yeah, those tricks are highly related to what we do, the main difference being that we don't require a priori information about the distributions involved in the program. Instead, we compute a density estimation of the distribution of branch conditions at runtime, which makes things quite general and fully automatic, at the cost of some accuracy.
As an aside, the combination "known distributions + automation" is covered in the Julia world by stochasticAD (https://github.com/gaurav-arya/StochasticAD.jl).