out of the 3 teams, they will initiate based on the team (of 4)'s total initiative. If you want Mei's to persist, put her on 1 of the 3 teams that has the highest overall initiative

Initiative wins.

I tried a little bit around, and it seems for me, that the middle team does they passive last, 1 buffing is top, then bottom then middle group.
Maybe you try having mei mid? or Gaara in top team?

The thing is, in ranked, all 3 team have the same total init. The init of all 8 ninja not on main team is the average of the four ninja on the main team (so those 8 have the same)
that said, I'm not sure how rounding behaves. If, for example, your ninja's init totals to 10001, then perhaps your main team will be fastest, as each of the other might be 2500.25 which rounds down to 2500 and then combine to 10000 for each of the other team. But... like i said, i don't know how that actually works.

A good ranked team should not be running 2 passive barrier users in the first place. That is probably why no system will be developed for this issue.

err... he's running two passive barriers?

I personally run 3. The thing is, the ones with passive barrier also have rly good high chakra costing AoE nukes, which really is the best sort of mystery in ranked, where targeted mystery tend to be * and battle tend to be long so high cost ones are good in the long run. The barriers themselves are merely afterthoughts.

Move Gaara 1st to another n then Mei. U have Mei's barrier.

Middle team is the barrier that procs last and will be the one that takes the field