There isn't one to my knowledge.
The first Spire run is always the hardest, but I believe you're intended to use the many time boosters you can get from there to make it easier to run time-wise. If your fellowship is on top of things and you're following along, you should get the following amount of 5 hour boosters from Spire Fellowship rewards by the time you reach the following tiers:
- Bronze: 7
- Silver: 7+11
- Gold: 7+11+15
If you and your fellowship are topping Spire every week, that's a total of 33 5-hour boosters you'll receive. That alone will let you practically zoom to the top of the Spire in a single sitting, absent any of the other (many) challenges. Then there are the numerous additional 1h, 2h, and 5h boosters you can get as prizes for each of the fights. Assuming all percentages are equal, you can expect an average pull at the following tiers:
- Bronze: (0.60*4*3) 1h, (0.25*4*1+0.65*5) 2h, (0.35*4) 5h
- Silver: Twice the value of Bronze, as the relevant rewards are duplicated in both quantity and chance this floor.
- Gold: Thrice the value of Bronze, as the relevant rewards are ALSO duplicated in both quantity and chance this floor.
So if you and your fellowship are topping Spire each week, you can pull an average of about (21) 1h boosters, (10) 2h boosters, and (4) 5h boosters, all rounded down. Since this part is all up to RNG, you can earn more or less than that.
Adding to RNG are the 3x5h boosters you might win when you open the blue mystery chests, and the 2x8h boosters you can get when you open the gold mystery chests, though boosters from
that source tends to be more of a letdown than a win IMHO.
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All of my (three) cities rely on the rather large amount of time boosters earned from topping Spire every week to keep things moving comfortably. As I've said before, getting to the top the first time is a bit difficult, depending on how well you've prepared, but staying at the top is far easier. Even more so if you've joined a fellowship that tops Spire each week, since the
real prize in getting that far is the many free diamonds earned from the Gold Spire Fellowship rewards. Such fellowships also tend to help out smaller cities that they've accepted in reaching the top since those delicious rewards are a group effort. Sometimes they'll even be rather vocal about all the tricks and strategies used to get to the top regardless of how far along the recipient player's city is.
I'm aware that this is a rather large post dedicated to answering a question that was never asked. But I needed to do the math on those boosters since I kinda also got curious as to where all the speedup things are coming from. Also, be aware that the numbers may have shifted a bit since there was some modification to the Spire prizes recently, but I do not believe those changes targeted any of the mobs relevant to these calculations.