This work addresses the problem of analysis and control of fork-join networks in the conventional Heavy-Traffic diffusion regime. Standard fork-join networks are feed-forward, which are relatively easy to control. Motivated by healthcare systems, we allow probabilistic feedback, which turns the problem into a challenging one. In our models, activities are associated uniquely with customers. They are hence non-exchangeable in the sense that one can not combine/join activities associated with different customers - this is the case in healthcare (e.g. emergency departments) and multi-project environments (in contrast to assembly networks). We introduce a natural concept of optimality for our model, and then solve for the optimal control, asymptotically in heavy-traffic. The central ingredient in the proof is the establishment of asymptotic equivalence between non-exchangeable and exchangeable dynamics.