The actual mechanics of the chemistry, I suspect, is advanced citing a recent (2019) reference noting some radical chemistry. My take is as follows:
First, heating in air (an O2 source) a boiling mix of NaOH and water in the presence of sulfur, I would argue may involve the reversal of the following radical reaction:
O2•- + OH• = O2 + OH-
where explicitly the reverse reaction, which was actually proposed as early as 1963 by Schroeter in alkaline conditions (per this Google Book source), is:
O2 + OH- = O2•- + •OH (Source above, Eq 5.98)
which apparently can be accomplished in the presence of high oxygen pressure, heat and alkaline conditions (as employed in oxygen-alkaline bleaching, see comments here. In the current text, the reaction equilibrium may be moved to the right with the consumption of formed radicals with say sulfur/sulfur compounds.
In particular, I suspect, the sulfur in heated water/OH- may acquire a charge upon heating and in accord with the electrostatic properties of a colloidal suspension resulting in the presence of some solvated electrons. Then, the formation of sulfur related radical(s):
S + e-(aq) = S•−
A path to the consumption of the highly reactive and non-selective hydroxyl radical (created above) could be:
S•− + OH• = S + OH-
One could also argue that the action of heat/light (see, for example, this Science Direct compilation) may reverse the above reaction leading to S•− radical.
Next, an interaction with oxygen from a 2019 semantic scholar article:
HS•/S•− + O2 --> SO2•- (+ H+) (Source Page 7, Eq (7))
SO2•- + SO2•- --> S2O4(2-) (Same source, per comment)
Then, per Wikipedia on dithionite which notes that dithionite undergoes an acid hydrolytic disproportionation to thiosulfate and bisulfite (presence of CO2 may assist):
2 S2O4(2-) + H2O --> S2O3(2-) + 2 HSO3-
[EDIT AUGUST 2021] Here is an interesting partial confirmation of my proposed mechanics. To quote the abstract from this work The Chemical Behavior of Low Valence Sulfur Compounds. I. Oxidation of Elemental Sulfur with Compressed Oxygen in Aqueous Ammonia Solution published in Bulletin of the Chemical Society of Japan, Volume 38, Issue 10, 1965:
- The oxidation of sulfur with compressed oxygen proceeds through the following sequence of steps: (a) The disproportionation of sulfur to both pentasulfide and thiosulfate. (b) The oxidation of pentasulfide to thiosulfate. (c) The oxidation of thiosulfate to sulfate and sulfamate through a series of complicated intermediates.
- Sulfamate forms only in the decomposition of trithionate.
- The overall reaction of the oxidation is prompted by a rise in the temperature, an increase in the ammonia concentration, and the addition of transition metal ions, especially copper ions.
So, a confirmation from a respected journal of my claim of the role of oxygen forming the long known reported products: pentasulfide and thiosulfate.
Also, an interesting reference to an apparent fostering role of transition metal-based radicals, where the citation of Copper is especially interesting as it engages in REDOX reactions over a wider range than other transition metals (like Iron) creating active species.
Now, what could be a possible path, perhaps re-reading my suggested answer will assist.