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 (see https://books.google.com/books?id=57noBQAAQBAJ&pg=PT717&lpg=PT717&dq=ozonide+anion&source=bl&ots=l2q2T3F5M1&sig=vN96PvvfnVU_NMsWppZ9w35_HYw&hl=en&sa=X&ved=0ahUKEwjKysOjxLnKAhVF8x4KHXeZBJY4ChDoAQgwMAg#v=onepage&q=ozonide%20anion&f=false ), 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 at: https://www.lindeus.com/en/processes/cleaning_polishing_grinding/bleaching/oxygen_reinforced_alkaline_extraction/index.html ). 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, https://www.sciencedirect.com/science/article/pii/S1010603018309729 ) may reverse the above reaction leading to S•− radical.
Next, an interaction with oxygen per a 2019 source (https://pdfs.semanticscholar.org/533e/9a0b2e5d938abc555e267f2f9b1a6a29f720.pdf ):
HS•/S•− + O2 --> SO2•- (+ H+) (Source Page 7, Eq (7))
SO2•- + SO2•- --> S2O4(2-) (Same source, per comment)
Then, per Wikipedia on dithionite (see https://en.wikipedia.org/wiki/Dithionite ), 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-