Sorry for the late reply. I might be misunderstanding your question but let me attempt an answer. You don’t really want to over-engineer the correlations between trees as that is only one of the key factors. Also important is whether the tree has signal (most of the trees will be weak predictors but we still want them to be at least somewhat predictive).

We want to avoid the case where we focus too much on producing uncorrelated trees and accidentally damage the predictive ability of the trees. Rather, we can rely on the knowledge that if we randomly create (using random forest’s algorithm) a large enough number of trees, many of the resulting trees will have low correlations with each other.

To tweak parameters like number of trees, max depth of the tree, etc., I would recommend using Grid Search. The best parameters is heavily dependent on the nature and structure of your data so a reasonably thorough search would be better than heuristics.

Hope this helps and thanks for reading!