So, the shoes have been removed. I didn't burn my shoes (+1), they smelled smokey (+1) and the sulphur looked as if it was nearly entirely consumed (+1).
Not sure if my dwell time of ~3 hours was enough. Also, I hear some people wet their items down to promote development of sulphuric acid which is how this works.
Anyway, they smelled a but smokey.
Finished pictures:
Green stuff still there, hopefully dead.

And the setup. Notice the charred square of cardboard. That yellow stuff is unconsumed and melted sulphur.

After this, the shoe interiors were wiped down with 70% rubbing alcohol to remove the hopefully inactivated mold spores, dried for just long enough for me to mix a mixture of 1 tsp. tea tree oil with a splash of alcohol to dilute. The mixture was painted on to each insole equally with an acid brush until the solution was all used up. Since tea tree oil both conditions and is a relatively powerful anti-fungal, hopefully the dilute solution will be able to saturate the leather a bit more deeply and prevent a re-occurrence.
I would potentially recommend this treatment, should it work, as it did not appear to alter the color or feel of the leather. I've experimented with bleaches and what not on some thrifted shoes before in attempts to re-color or to figure out how to combat this problem which I also experienced with a pair of Church's with very bad results. I have not yet had a pair of shoes which did not dissolve using the bleaching method. Also I am unaware if Cheaney and Church's are currently related/working together but based on my reading this does seem like an issue with improperly tanned leather. Both shoes were purchased concurrently from the same shop.
In total, this cost approx. $3.00 in materials (sulfur purchased from ebay), a handful of common household materials (basket, duct-tape, alcohol, paper towels, acid brush and a ceramic bowl) and trash-picked items (the bowl I used and a large box), and took perhaps an hour - including the trash-picking - of total active time.
The tea tree oil was left over from a previous project, but also can be had for less than $10.
So, $13.00 to fumigate and prevent, with enough sulphur to treat at least twice more.
Waiting is the hardest part.
But notice, this was not attempted to combat odors and/or long term mildew issues but an active green mold outbreak.
Time will tell if this worked. I'm optimistic.