I think the term for NT managers should be for 2 seasons with a chance for a bonus team if the NT qualifies for the finals. This would make the normal election time for most countries at the start of the season following the continental qualifications. This will give the new manager a chance to develop his squad before actually starting qualification.
A team that plays in the finals will have a reasonable squad that should be able to go directly into qualification with its new manager, so the delayed election and transition will have less of an effect.
I think the problems with NT managers going inactive is largely a one-time thing, associated with the newness of BB, the newness of many countries, and the newness of NT, so that a more elaborate scheme for replacing NT managers is not needed. Holding new elections in most countries at the start of Season 4 will replace most of the NT managers that have gone bot or are inactive in managment of their NT.
In the future, BB could hold special elections in case the NT manager does go bot from BB. I don't think it is a good idea to let the NT manager quit, since it will give an incentive for other managers to try to make the NT manager quit. I also don't like the idea of a popularity poll being used to drive a NT manager out. Instead of the original election settling matters for a while, you could have losing candidates and their supporters continuing to try to replace a newly elected NT manager.
Since the current NT managers were elected for a 2 season term, those that did not qualify for the finals could be given the option to resign, in which case they could run for a new full 2 season term. So instead of a lame duck season, they would be playing scrimmages preparing the team that they will continue to coach in qualification.