I think you have to for Tournament first to contest the Prizes, since Princess and Followers can really change the game in engine-friendly boards with no other cursers or +Buy. There's always time to pick up a few Saboteurs later.
I would open with Treasury rather than Cartographer. It'll help you hit $5 regularly, and once you pick up another Treasury with a Tournament or two, you're pretty likely to get an early Province, or at worst an early King's Court. With Treasury/Courtyard, you've got much better odds of getting a KC in your first shuffle, which would give you a big early lead. I feel like unless you can use Cartographer to line up engine pieces, or have a means to draw the good cards to put back on top, it's almost like a glorified Warehouse that doesn't decrease your handsize. I agree cycling is important, but there's nothing on this board you really need to play as early and often as possible (e.g. cursers). Once you have a KC or Tournament + Province, Cartographer will be useful to find them, but you should focus on getting them first.
