Without seeing the full setup, I'm guess a bit here, but I think if you did this, it might work:
Top Campaign - List Processor:
Smart List: Member of Smart List IN "Big Send List"
(note: you may want to pre-process this by sending everyone to a static list first, which will lower processing time)
Flow: Request Campaign Choice 1: if Member of Smart List IN "Country 1", Call "Country 1 Send" etc
Schedule: Batch, Now.
Send Campaigns:
Smart List: Trigger: Campaign Is Requested by "Marketo Flow Action"
Member of List IN "Big Send List Country 1" (this constains the filter to ensure only those go out)
Flow: Send Email IS " Email Country 1"
Wait Step: Wait Until....X time on X Day
Schedule: triggered
But the problem here is you'll need to kick off the Top Campaign at the correct time to ensure this works well.
You may be better off splitting the Big List into separate static lists, then activating each country campaign one at a time on a scheduled basis. I'm not sure a Traffic Cop is your best choice here.