My city is new (still in chapter 4 but coming up on 5), and is pretty compact (I just popped in a 21st expansion today because of sale and ... lays potato chip effect). What I've noticed having the biggest effect on the size of my stacks so far is the relic boost and squad size upgrades. I'm not saying other people are wrong about how the formula works, but I'm guessing that different things have more of an effect at different points in the game (either because of math such as maybe a "(# expansions - X)" instead of "# expansions" somewhere in the formula or just because some variables grow faster than others at various points of the game, such as relic boost not growing past 700%).
So for example we just finished the elixir tournament. My boosts are marble, crystal, and elixir. My elixir boost grew substantially to become my highest boost at 592% and I had one squad size upgrade (a 33% increase from 90 to 120) as well as two main hall upgrades (these are not found in the formula, but we don't know for sure there is no effect), but no other substantial changes to my city (this is before I popped on the expansion). I have no AWs yet. I observed that the convince cost in Spire and battle stacks were close to twice as big as they had been the previous week.
Unfortunately I'm doing two more squad size upgrades this week, so we won't be able to determine whether that extra expansion had a significant effect on tourney and Spire costs.
Edit: The ironic thing is that Spire and tournament don't cost t3 goods for me yet, so my Elixir relic boost is only penalizing me without directly helping me. (I could cross tier trade for other goods but I prefer not to.) I've actually passed up some elixir relics in my MA to avoid making my elixir boost even larger in comparison to my t1 and t2 boosts. This is something that the new tournament relic format will help with -- keeping t1, t2, and t3 boosts for a given player more even. I wonder whether that is part of the thinking behind the decision.