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After discussing with @gcol33, via email, we realized couplr is not a good fit for usage in this package.
However, the discussions were useful, as this problem is already solved with a method "known as Pocock-Simon minimization, generalized here from two arms to k batches: one pass over the samples, optimizing exactly what check_index measures instead of approximating it by chance." I'll open a different issue for that.
This package has some academically-backed method implemented to matching samples.
Relevant are this comparison of packages: https://cran.r-project.org/web/packages/couplr/vignettes/comparison.html
couplr