Adaraneeya Abhyankara Mahodaya,
Thanks for your detailed clarifications. I feel since the Sutra 8/4/58 is silent on the issue of Anusvaara followed by श्, ष्, स् , ह्, it seems to confirm that Anusvaara retains its original native sound. But I don't think Anusvaara in case of हंस converges more towards the Nasal ङ् of the कवर्ग.
My thinking is native sound of Anusvaara is by closing in of the teeth and the lips, which is not done during the intonation of हंस. Only the lips are closed, which results in the sound of म् only. This is also validated by the way it is intoned in Vedic tradition I belong to, which is Krishna Yajur Vedeeya Taitrrya Shaakhaa.