gentlemen, ladies, and all other distinguished citizens of the neath, I have, for reasons most unwise, found myself in desperate need of a great many searing enigmas, and have as such found, what I believe to be, the most efficient grind for them possible, with perhaps the sole exception of buying and offering orphans to tigers, (or use of fate)
this process is quite complicated, available to mid-to-late game players who have started the Great Hellbound Railway, with multiple distinct parts, so if anyone has any way to improve any part of it (which don't require echoes or fate), than let me know.
part 1: The enigmas themselves:
contrary to most guides, we'll start with the end step, and then work backwards to see how we build up to it, for this grind our enigmas will be sourced from the University's department of Infernal Rarefactions, accessed via the following storylet and options:
Shadowy Dealings at the University --> Visit the Professor Denuntiatus of Infernal Rarefactions --> Manufacture Searing Enigmas.
This requires you to have access to the university (see here for gaining access to it), and costs 1 AP, 25 Uncanny Incunabulum and 20 CP of Connected: Benthic, to produce a variable number of Searing Enigmas, this also requires passing a Broad 200 watchful challenge (failure provides only 1 enigma) and higher watchful raises the maximum number of Searing Enigmas produced, so maximal watchful gains and equipment is recommended. see here for further information.
part 2: Uncanny Incunabulum (the most complex part of the grind)
part 2A: Newspaper publishing
To achieve the above steps, we will need to source Uncanny Incunabulum, to do this we will be using the newspaper grind, this will require having access to a newspaper (see here) for both starting a newspaper and further information on the newspaper grind itself) you will also need at least 1 of: Jericho Locks station, or a Hell-Scarred Gondolier, (see here) and here for information on each)
this will cost 1 whirring contraption, and 13 AP, during this process, choose as many of the following options as you are able:
The predator beneath, A travelogue of the Hinterlands [req: Jericho Locks station], An in-depth report on the Fourth City, Interview the Manager of the Royal Bethlehem, The Hell-Scarred Gondolier [req: The Hell-Scarred Gondolier], Something unlikely about the Home Secretary, Letters from Downside, An interview with a colourful character, Spirit photography.
if you lack 1 of the two required qualities, you will also need to to choose Do you have insufficient balderdash,
Either way, the important part is that get to the last step of the process with at least 104 outlandish copy, enabling you to choose The finest kind of madness, granting 4 Extraordinary Implications and 118 Journals of Infamy.
Journals of Infamy can be converted into Extraordinary Implications at a 50->10 ratio for 1 AP and 5 CP of Connected: Benthic, (as a bonus, this will also variably provide 100 glim, or, rarely, 2 Storm-Threnodies, see here)
Extraordinary Implications can be converted into Uncanny Incunabulum at a 25->5 ratio for 1 AP and 20 CP of Connected: Benthic, (as a bonus, this will also variably provide 200 Nevercold Brass Sliver, or, rarely, 1 Nodule of Pulsating Amber, see here)
As a further bonus, both publishing a newspaper and converting Extraordinary Implications produce making waves (5 CP from publishing, a highly variable amount from converting, see prev link)
part 2B: Whirring Contraptions
publishing papers requires Whirring Contraptions, these can be obtained through Searching out a Missing Woman at Wilmot's End, by finishing with The carpet bag, see here for accessing Wilmot's End, and here) for further information on grinding Whirring Contraptions) this gives 2 Whirring Contraptions for 11 AP, presuming you have high enough watchful and/or persuasive to pass all checks.
part 3: Connected: Benthic
Journal conversion, Implication conversion, and Incunabulum conversion, all require varying quantities of Connected: Benthic, to source this, we begin with Hunting Bees in Old Newgate, found at the university, starting this process costs 1 AP, we will want high watchful, dangerous, and Mithridacy.
One of Set an ambush or Sow carnage will always be available, depending on which side your on, these give 25 bees and will be our usual action, occasionally either Betray both sides or Commune with the bees will be available, these grant 31 and 33 bees respectively, and should be taken when they appear (assuming you can pass their checks) all of these option cost 1 AP each (see here) for further information).
Once a large enough quantity of bees are obtained, choose Send a small amount of Bees to Hell, to exchange 50 bees for 3 Muscaria Brandy, and convert all remaining bees into Foxfire Candle Stubs at 1->10 ratio for 1 AP.
Foxfire Candle Stubs can be converted into Flasks of Abominable Salts at a 1000->105 ratio, for 1 AP.
Using an Endowment of a University Fellowship, we can spend 15 Flasks of Abominable Salts and 3 AP to gain 75 CP of Connected: Benthic. (note: the Endowment of a University Fellowship can only be obtained by purchasing it from the Bazaar, however I still consider this an echo-less grind since its a one time purchase rather than a continuous need gain and spend echoes).
Addendum: The rat market
The rat market is available on Friday->Sunday, its demands change each weak, and it can accept various high value items, at no AP cost, for large quantities of rat shillings, which can be spent, at no AP cost, on tales of terror, at a 7->1 ratio, the rat market requires a once per week 3 AP cost to enter(see here) for further information).
tales of terror can be substituted for Journals of Infamy, converting to Extraordinary Implications almost identically, the primary difference being that it costs Connected: Summerset instead of Connected: Benthic.
Connected: Summerset can be acquired in an essentially identical manner as Benthic.
depending on the rat markets demand and your own inventory, this can very well be worth it.
Final AP cost analysis: conservative guesstimates ahead
The exact amount of Searing Enigmas generated at the end step is somewhat random, but lets say it averages about 4 for sake of analysis.
this whole process costs 45 CP of Connected: Benthic, (assuming you don't use the rat market) it costs 8 AP to produce 1000 Foxfire Candle Stubs, (though this becomes more efficient the fewer cycles of Bee Hunting you do, as 4 AP is spent per cycle just to enable and finish this cycle) + 1 AP to make that into 105 Flasks of Abominable Salts, which is enough for 525 CP of Connected: Benthic, slightly complicated by the fact that you can't gain Connected: Benthic this way while above 19 levels of it, though its not actually caped there, so the math should still work out, that adds 21 AP cost, bringing our current total to 30.
30 AP for 525 CP, which is enough for 11.6666... full cycles of conversion, we'll call that 11 and add 11 AP to our total for our end step, bringing us to 41 AP cost for 11 cycles.
To achieve 11 full cycles, we need 275 Uncanny Incunabulum, which requires 1375 Extraordinary Implications.
15 AP gives very rougly, 24.6 Extraordinary Implications, adding about 838.414634146 AP per 11 cycles, (again very roughly).
quickly adding in 5.5 AP per cycle to account for whirring contraptions grinding, and we get a total of 939.914634146 AP per 11 cycles.
939.914634146/11/11 brings us to 85.4467849224 per 1 cycle, 85.4467849224/4 brings us to an extremely rough 21.3616962306 per 1 Enigma, for conservation's sake lets call that 22 AP/1.
Now, this math is highly approximate, and almost assuredly I have made some glaringly obvious mistake that will embarrass me once pointed out.
its probably better to just buy orphans and give them to tigers, I haven't checked the math on that yet, however I am proud to have put this effort into this little guide, no matter how useless it actually is, and if anyone out there cares enough about this stuff as I decided to, please fell free to add corrections to my awful math, or edits to my janky methods.