Just noodling out a possible way to implement the OP point...
1) This can't be implemented as simply posting the lowest value of the available Provinces, as the highest available province is always immediately available (unless you can actual complete a full round of provinces). This is easily dealt with, by ignoring the status of the highest province if that is at least Province #2.
2) This will work well if you clear your personal n provinces every round.
3) This will work well if you intend to clear your personal n provinces every round, but don't manage to do all n at once.
4) This will fair poorly if you do unusual things, like I occasionally do during Quest Events or modern FAs. For example, suppose I intend to clear 16 provinces for all 6 rounds. But, to service a Quest or to gain a badge, I might do provinces 17-20 for 1 round, Now, the status of my 1-16 provinces will be hidden by a cleared-for-round-2 province 17.
For #4,maybe this could be implemented by giving the lowest time of the province with the most completed rounds, or maybe the lowest times of the province with the highest or next-highest completed rounds.
Easier to logic, and easier for the user to understand, but requiring an interface for user input, would be to somehow let the user specify how many provinces are important, from which to report the lowest timer value. For example, if I intend to clear 16 provinces for 6 rounds, I would want to tell the game that 16 is the magic number, regardless of if I do a couple of higher one-offs. This could be with a dropdown or number entry field somewhere, or with a toggle flag that I set on the 16th province, kind of like the Favorite indicator for Ancient Wonders.
most of the time I keep checking but I still had to wait, then I forget and that's why rarely I can do the 6th round.
