I'm still new enough to not have as good a solid feel for how far I can push, especially now that I'm getting dwarven armorers and 2x2 "unleashed" boost expiring buildings in the Spire and occasionally in the MA, so others' mileage may vary.
I fight until first Defeat and then cater, and measure my progress in how many more steps I can take fighting per week before catering, in both Tourney and Spire. I'm playing on iPad, so it's instant batch fights, which pleases me fine. This approach seems to net me performance well above grade in the tourneys (over 3000 at starting Chapter VII, and over 2500 in Chapter VI) and I'm greeting the Frog or a little better each week in the Spire. That said, I could stand to take a little breather sooner in one (my slightly larger) city, where I run at close to dust in some troops, and use time boosters to quickly train batches of troops just to keep up with myself. If someone else told me of this issue, I'd say cater just a little sooner and build up some backlog of troops. Perhaps I'll take my own advice, grin!