Do deeper Strata give more Crowns/Heat?
Yes, every tier of depth has more potential crowns and heat than the last. Mostly because of the more difficult monsters.
The even-numbered strata always give more crowns and heat than the odd-numbered strata - basically, once you reach the clockwork terminal (4, 13, or 20), the loot kicks into high gear (and goes back down when you return to an odd-numbered strata.