Not having read cold case yet I'm at a disadvantage in info here. But I have a problem with the idea sidhe cannot mate and produce... What was the point of the sidhe wars or how did those they where based from manage then?(I.e. The Greeks)
I think the caveat on them doing so is in their nature, they don't have or use the primary 'elements' that make procreation possible above physical function. Harry and a spirit procreate via love connection not physical act. So if such acts are foreign to them...?
Not sure how the tributes work, but that's them sacrificing themselves yea? The old school worship/ giving of yourself/ sacrifice. It was that element that made Bonnie, it's that element the tributes actually contribute?

Captain Kudzu” was working under Mab’s orders.  Having been deemed “sufficient” and since she ordered someone to bring Molly in. (This tilts my theorizing away from the theories that he was a nemesis agent, since Mab was actively trying to recover from nemfection in her ranks when she assigned him.  But that's not a given.)

now see, I've never thought these were mutually exclusive.*upon farther thought, it's my belief mab intentionally puts things in harrys sphere of existence knowing full well they may or probly are Nfected. Besides this, we know Cat Sith. But what purpose did mab have putting the eldest of his race to work as harrys batman when any other could have worked? I can't remember the difference between watsonian and doyalist but considering that precise character becomes a threat in the very same book, I find it highly likely she knew and wanted them to cross paths* Mab sent the fetches to do just that, fetch. But did she? The captain says he has worked for the queen of whatever since before human memeory, but if before human memory consigns one to oblivion, how is this possible? He referred to the original. This is a case of the embalance causing MW to release that which was contained beyond intentionally, to preserve a balance when necassary(at the time mab had the WK locked up... Locking up an element of the winter court that is supposed to have freedom of Will was why the fetches were sent at all I think, otherwise the winter knight could do) Also, as the fetches are one of the only fairy creatures who possess no body on the mortal plain, they lack that 'soul' or choice related to being part mortal, they were set up that way to eat the Nfection that can be perceived in PG that Molly hasn't had to deal with since, cause they ate that Nfected bit of soul right before Harry got to the top of the tower. Case  in point, mouse's reaction to Molly when N is potentially present, or fearbringer specifically. The whole explaination for how the fetches are summoned shows
1 anything on par with... And I can't remember if the lady qualifies or not... The queens can Breach the NN from the other side,
2 beacons are a must, having something to guide oneself.
Might add a few more after I go back over...
But from what we now know of outsiders and N, there is a fearbringer, Molly was set up to use fear, to become a fearbringer.... They made her into the beacon for the outsider to find his way back, add on the mortal magic of change and yea. Same being in both PG and CD. Pretty sure both the scarecrow and FB both had a moment of recognition with Harry too.
Simple to think one of the outsiders allies goals is to reintroduce these things as part of reality. Ties into the idea Molly's 'fearbringing' helped form the mask FB actually uses to exist in CD. It's like the mirror, it mirrors things incompletely and not entirely accurately but FB has the same form and function of Scarecrow. Like a shadow/mirror... Also, scarecrow in batman is called the master of fear and was actually 'something' crane(can't remember his first name off of top of head, edit in later!) who madrigals identity pays homage to as Darby crane. Also connected to ichabod crane from sleepy hollow, a story that had his own fearbringer of sorts. So all these elements connect, right down to Harry being the metaphorical and literal batman lol.
I haven't gone over all this in a couple years, nobody seemed to notice when I did then though... So if it seems incomplete or you have questions, then shoot. I might not have the right answer, but chances are I got something...

2)  Summon the Murk during the Phage attacks
A, the cold nature of the Murk wards in these attacks screams Winter
B, Harry does briefly sense something familiar about the magic involved when he reaches out towards it

Negative:  It's hard to imagine Harry submitting to casting a spell that would facilitate the carnage the phages were wreaking, and also the blowby damage that was done by the confused people.

your forgetting one key element TTH has to make sure of, his concurrent alterations do not end in the premature death of Harry himself and other unwanted effects, like Molly going bad, getting killed, ect. Same reason Thomas seems to follow him in the background after the 'LC incident'. Been awhile again... But if you notice by the time Harry arrives past the murk he's no longer afraid of the fetch, he's pissed directly because of the mayhem those extra seconds caused. So this is one more 'stop past self from dying' action that was actually all caused by an alteration of time regardless of if time travel Harry did it or GK, the moment Harry learned of black magic early it changed everything that had been going to happen, but the effect had to be controlled to keep it from ending up worse. Also not certain but

4)  Probably something big at AT before the PG dungeon crawl party showed up.
To be honest, the main reason why think TTH was involved in the battle PGH saw the aftermath of is because I really want some closure on what happened here, and this is the ideal way to get it.  I WANT I WANT I WANT.  There maybe if I say it loud enough I'll get it.  (Griff has pointed out to me that Jim has promised us more story about what happened at AT)

if TTH did it, then the current 'cascade' had Harry becoming a denarian, which from MM seems likely enough. This would also explain mabs anger at Harry over the assault, her seeming double ontondra to me, implying one day he himself would pay, not for the second assault, but for the first one he may have done... Can't take balance on someone who hasn't done what they did yet I think...

5)  Fix Little Chicago the morning of the 2nd day, while Harry was out of the Appt. at the Hospital with Murphy, Bob, and Mouse.
Evidence for TTH kinda stacks up, not that there aren't alternate possibilities.
See my LC fix timing topic linked in the background post above for the evidence as to the timing
TTH was intimately familiar with LC.  And had the chops.  And knew it was there.  And could get in (not as big a deal).  All those things listed at the end of PG.
I have felt deep down for a long time that if TTH did it, he did it because a functional LC was absolutely vital for him to do something HE needed to cast a spell for.  This binds LC's fixing tightly to the "tropish TTH goals"
The Mystery of who fixed LC becomes necessary to preserve the space time continuum!
I'll just keep adding things to this post as I remember them or find the pertaining question in the first post, or if someone replies directly....

the cascade! Harry wasn't going to use little Chicago early before GK sent his note, it pushed up his actions and would have caused his death, so while future Harry could have done, current GK could have also if he was looking for echoes that he caused passing along the note... Personally, all the energy to one spot... Makes me wonder if TTH didn't arrive through it, it's basically I big focus for a time and place, Chicago, for only as long as the model was kept accurate, so thaumaturgically it could connect through time and space and be the 'dolorian' in question.
I'd think originally, he had given in to lash finally before he used it. In the current timeline he refuses in the moment...