Thanks to /u/conradev (who, I guess, unlike me, did not trust the people who were saying extracting the dyld shared cache didn't work and just did it... apparently, everyone else was using some third-party tool, and if I had just ignored them and used the tool from Apple that I'd been using without issue now for years, I would have been able to work on this more yesterday :/), we now know exactly what causes the "invalid" URL issues (not just the proximal cause, which we've known for days, but the actual exact check in MobileCoreServices that is responsible for deciding that these URLs should not work correctly).

I have put together a fix for this as part of the package Patcyh, which is already solving a similar issue (and, in a very real way, "causing" this issue... frowny). This fix is not at all the kind of normal/sane modification I generally would try to do in this situation for multiple reasons: one of which being that Patcyh is quite simply not allowed to rely on Substrate, and yet this is a modification that is screaming to be done using Substrate; and another being that the entire concept of this package is only due to other corrections (and so in a perfect world we wouldn't have this package at all, but, well: "mistakes were made").

The primary concern is that in wielding a massive hammer to fix this problem, I have actually caused collateral damage. In fact, I posted a similar thread something like five hours ago, someone tried what I had working then, and it was pretty fatal. It is trivial to undo this if you have OpenSSH installed (just downgrade), but they did not :/. So, if anyone is willing to debug this, I will say I've tested this setup myself now quite a bit (before, I was essentially relying on someone else to do most of the testing, as I was not in a position to actually test much of anything), and I'm actually feeling confident in how I narrowed it.

Add this repository to Cydia, and upgrade Patcyh:

http://apt.saurik.com/beta/patcyh-url9/

(I am now going to go to sleep for a few hours, and hopefully not wake up to everyone screaming that their device literally caught on fire; but, if that happens, I guess I hope it leaves a scorch mark in the shape of an Apple logo in the center of the screen, as that would be awesome.)