Okay, that's much less than I thought, because of a wrinkle I had not thought would go that way.
First, my quibbles...
So, you do 27 provinces first round, then 3 provinces the remaining 5 rounds. And over the 9 weeks, those 3 provinces would shift, so you went to completion on the first 27 provinces over those 9 weeks, equal to having gone to completion in 27 provinces in one tourney old style. But, you had to do 24 first round provinces extra for 9 weeks, so you are still doing 216 extra provinces (albeit easy ones) every 9 weeks, Which means it costs more.
Now, that overage can be reduced, since you don't have to do 27 first-round provinces each tourney, only as many as necessary to get to the three provinces that have your target. Still extra, I think 108 instead of 216...
Lastly, long term, whether you're draining your troops all at once every 9 weeks, or gradually over those 9 weeks, troop production will have the same 9 weeks to keep up with demand in either case, so no better or worse chance. Actually, you possibly have a more problems with gradual, as if you have a particularly bad week or two, you might run short of a particular type mid-9 week, which won't happen mid-all-at-once.
Now, to the wrinkle I had not thought of. I had assumed that the rotating relics would shift province-to-province within a round, as well as shifting round-to-round. I had not considered it possible to open many provinces first round allowing vertical specialization on particular relic types.
Whichever way it goes, it kind of waters down the concept of "this is a Marble tourney". Okay, the first province, first round gives Marble relics, but after that? Most people's efforts in a 'Marble' tourney will end with them getting more relics of a single non-Marble type then Marble, and equal numbers of non-Marble to Marble relics. Okay, the bonus relic rewards for group participation will be Marble, so there is that...