I overreached the first night, just to get a feel for how much harder it gets as you go out, and went out to 8 provinces. The biggest jump was from 1 to 2. After that, it didn't really seem to get noticeably harder.
This morning, I went out 6 provinces for the 2nd star. A battle in the 6th province chewed up my troops, so I finished via negotiating.
I'll look at the 3rd star tonight before going to sleep.
Largely, I found catering the first province to have costs equivalent or less than losing a single unit, so that's been better to cater. The rest seem better to fight, until I run out of troops. (And until I get that sorceress upgrade, they're not helpful as a support troop.)
Ultimately, the limiting factor is going to be my training speed. I'm concerned that I'll sink too many resources into Tournaments and not have enough to progress, and progression gives much better rewards than Tournaments. So, I'm seeing this mechanic as a safety valve for people who have too many resources/troops and want an expensive way to turn that into something useful. (Just like the wholesaler does for gold/supplies.)
Oh, and where can I look up what relic type next week's tournament will be? If it goes in a circle, it should be known, but I don't know where to find out.