80% seems like quite good odds, in my opinion. In 2.5/3 weeks, 14 Permits hardly seems like impossible. I’m hardly close to your level, but I suppose if you want to be more efficient, you could use second chances to ensure success on the heist so that you don’t have to do more casing than necessary.
Some calculations, for estimation’s sake, assuming you already have enough casing to attempt, and only need to accumulate it after you use it:
18Casing/5Actions = 3.6 Casing/Action. At 32Casing/Permit on success, this is 8.88 Actions/Permit. No strings attached, unless you count the few actions, Making Waves, and Society Connections you might spend accumulating Hastily Scrawled Warning Notes to ensure a success.
Doesn’t get much better than that, in my opinion. Even if you only checked FallenLondon twice a day, that’d be 4 Permits each day, with energy to spare for Opp Deck cards. I’m probably messing up the calculations somewhere here, but I’m sure you can probably get the Permits pretty fast.
The Antique Mysteries might be a bit harder. Again, though, with the same Action/Item conversion as the Bazaar Permits, there’s no other reliable source that gives em to you that good. If you have a Trade Secret or are close to one, I guess you could trade in 10 Actions and the Secret for 5 Antique Mysteries, which offers a smooth 2/1 Action/Item conversion, but requires that you have the secret already. Hopefully you’re close on that front?
Either ways, when all is said and done, you need 41 Mysteries + 14 Permits = 45 Items*8.889 Actions/Item = about 400 Actions. Assuming you check FL twice a day without Exceptional Friend and get 40 actions a day overall, you could have it all neatly tied up in about two weeks, give or take Opp Cards and whatnot. With Exceptional Friend, halving this time is not unrealistic, and if you check more often than 3 or 6 hours at a time, during a day, this grows a little more efficient.
Sorry for the long ramble; I kind of like math sometimes, I guess.
TL;DR: You got the best way to obtain Permits and Mysteries is stealing them in the Flit, barring converting Trade Secrets. If you steal diligently and use Second Chances as needed, you’ll have it done with time to spare before the Wicket closes.