@Huor
Keeping a good inventory of the boost bldgs is tougher at your level in the game. You won't be able to get my results for some time, but start thinking along the lines of using the same set of boost bldgs to do both the tourney and Spire.
I've been playing the Spire since launch (a bit over 2 yrs ago) and I've increased my crafting considerably with the rewards from the Spire. But, my biggest advantage is being able to use them conservatively and get maximum benefit while the boost bldgs are active. With an advanced TimeWarp AW (which isn't even available until the end of Ch14) and a lvl 10 polar bear, my cooldown between tourney rounds is zero in one city with a lvl 30TW and 40 min in the other (lvl 28 - I'm working on it, lol!) Even low level polar bears can help some. Level 1 could make it so you can reasonably fit in 6 rounds every week time-wise.
What I've figured out (haven't been able to coordinate my life to actually accomplish it yet
) is: It is possible to do 2 Spires and 2 tourneys off one set of temp bldgs with zero cooldown and a decent amount of time boosters. If your FS gets the Silver trophy, the FS rewards give back enough time boosters to replace all it would take to run through the entire Spire, so any you win in chests is still a net gain.
The idea is: Wait until Friday, place the bldgs, feed the Fire Chicken and do the Spire. Feed the polar bear and you've got from whatever time now until the tourney ends tomorrow (Saturday). You can do each province round one right after the other whenever you have time to knock some out until you've done whatever you wanted to for that week. The Spire launches Sunday: Feed the Fire Chicken; if you finish the Spire by Monday at the time you fed the bird on Sunday, you'll conserve pet food, too. When the tourney launches Tues, the temp bldgs will still be active, including the polar bear (its feeding lasts 5 days). Feed the Fire bird again and you have until Wed (at the earlier of either the time you placed the bldgs Friday or the time you fed the chicken) to get the tourney finished. 2 Spires, 2 tourneys, one set of boost bldgs and 4 pet food.
At this point, I'm still sometimes finishing the current week's Spire on Friday (thus...running out of time...) but that's because I let event quests dictate when I do Spire/tourney and I can't seem to get on the right schedule...yet. I'll get there. I'm usually doing the entire tourney on Fri/Sat, so I know that part works. Part of it for me is in Spire and wanting to do all manual fighting...very time consuming...Maybe once I get the other city to zero cooldown I'll be able to do both tourneys quickly on Tuesday; that would let me set out the bldgs Thurs night and knock off some time in the Spire. Manually fighting 2 Spires is just tough to fit into a few hours on Friday before it ends.