Algorithm for Projecting to a Specific total QN

Not urgent, but an algorithm which would be of great general use would be one for projecting a tree tensor network or MPS into a specific total quantum number sector. Here is a brief outline of how this could work, taken from my answer to this forum question:
https://itensor.discourse.group/t/project-product-state-to-fixed-quantum-number-qn-conserving-mps/689

Set up a DMRG-like calculation but without a Hamiltonian (similar to setting $H = \mathbb{1}$). Then in the “core” step of two-site DMRG project the wavefunction tensor into the total QN sector you want and SVD back to adapt the bond index. Then sweep to every pair of sites and repeat. To code this in the most efficient way, one can use the orthogonality properties of the MPS to not have to deal explicitly with the right-hand-side basis at all (it cancels with itself). Also I think one can prove this algorithm converges in a single pass over the MPS.

Start with the linked ITensor Discourse answer and the issue's DMRG-like outline. Define an algorithm for projecting tree tensor networks or MPS into a specified total quantum-number sector, including the proposed single-pass convergence behavior; done means the projection works for the stated network types and target sectors.