Mannich reactions with sulfur

So I'm studying condensation reactions such as the formation of hexamine, and have come across an interesting subclass wherein one or more of the nitrogen atoms is replaced with a heteroatom or heteroatom-based substituent group.

Instead of a 3:2 molar ratio of formaldehyde to ammonia, a 2:1 molar ratio of formaldehyde to sulfamide— H₂N-SO₂-NH₂ —produces this condensation product:

This condensation takes place in acidic conditions rather than alkaline; I'm under the impression that alkaline conditions result in a long polymer rather than a cage.

Unlike sulfamic acid, however, sulfamide isn't readily available to the amateur, and the standard preparation method (mixing sulfuryl chloride and anhydrous ammonia) is beyond the reach of amateurs.

Would it be possible to, say, combine sodium sulfite, an acidic ammonium salt (such as the hydrochloride), and 37% formaldehyde to generate this compound in one pot?