I think that some eliminated NT coaches in HT do OK, but you still have the situation with the U20 where the 2-year mandate works like this: (1) win election, (2) build team quickly, (3) start qualification two weeks later, (4) after elimination if you're a nice guy start building team for next qualification with younger players (5) end term.
And it should be remembered that when NT were started in HT, that there was no qualificiation, so coaches were elected at the start of a 1-1/2 season period of friendlies before the actual competition began.
If you're concerned about overlapping elections, hold the elections after completion of the repechage. The only issue then is what to do in the 12 (of 74) countries that are in the finals. You could defer the elections in those 12 countries, or you could defer installation of the newly elected coaches.
Note that this would imply election of the initial U21 coaches in perhaps 3 weeks, with the teams playing scrimmages this season. The initial NT coaches would then be considered to have been elected late in the cycle due to this being the initial implementation of NT - unavoidable, but not necessarily desirable.
Or alternatively, you could wait until Season 4, Week 5 to elect the 2nd NT coaches, and hold off electing the initial U21 coaches until Season 5.
This would mean that WC I would be in Season 4, WC II would be in Season 6, and U21 WC I in Season 7.
My concern with being able to fire a NT coach is not that it is as easy as I seen to point out, but that it is so easy as to be possible at all. If someone screws up really bad, it is better for the BB to remove the coach.
Otherwise, you will have either (1) countries voting to get rid of their coach, and then the BB deciding whether it is really warranted, which will produce a lot of heat in the forums, but not any resolution;
Or BB realizing that the NT coach hasn't logged in in 5 weeks, and asking the voters whether they wish to remove the coach, which trivializes the whole process of voter control.
If you still want to implement a vote of no-confidence, I would first make sure that the winning manager received a majority vote. So perhaps you could have registration of candidates for a week before an election, and let them include a manifesto.
Voters may rank (all | 3 | 5 | 10) candidates. If any preference is excluded, the other preferences move up in the ranking. Voters may change their preferences at any time. If a voter has not voted, or all their preferences have been excluded, this might be highlighted on their menu (same as if you have BB-mail or a scrimmage challenge).
3 days: Top 7 plus any over 6% (16 max)
4 days: Top 5 plus any over 12% (8 max)
5 days: Top 3 plus any over 18% (5 max)
6 days: Top 2 plus any over 24% (4 max)
7 days: Top 2.
8th day: Winner announced
With preferences, those who don't log in daily won't be excluded from the final decision, even when candidates are eliminated each day.
Then BB should remember who voted for the winner. At any time, anyone may express confidence in the coach, but only the votes of those who elected him count. It might even be hidden from each user whether they voted for the winner or not, and so the confidence level in the coach might only be updated once per week. If support drops below 50%, the coach is gone.
Managers who quit BB would be excluded. So JuicePats was supported by 63 voters, and let's say that 6 of those eventually quit BB. As long as he as the support of 29 of the remaining 56 supporters, he keeps his job as USA NT manager.
This means that those who are disgruntled with the election results can't turn around and start trying to replace the winner.