July 10th, 2014, 11:44 pm
At the risk of stirring memories that some people may prefer to leave sleeping, this probably calls for a Gaussian copula. Use your Cholesky matrix to generate a set of correlated normals, and then transform the ones that needs transforming into triangulars. That is mechanically simple and would seem to satisfy your basic requirements. Whether it makes sense is more of an empirical question.