Background
I'm an infrastructure support night team leader for a very large IT services company in the UK. Due to the requirement for 24/7 support that most of our clients have, the support teams are on 12 hour shift patterns, 4 days on, 4 days off with no rotations - this means the night team does not transition to days and always works nights, an important factor to bear in mind. The shifts are regarded as a huge perk by all staff who work under them, including me, and the company loves them as it allows them to achieve good coverage with fewer staff than a standard 8 hour shift would.
Problem
Last year, our venerable and highly esteemed infrastructure support manager (my direct boss) retired, and was in due course replaced by an outside hire, a much younger and evidently less experienced chap. The company is currently focusing on efficiency and cost-savings for various reasons, and the new manager has really taken this to heart. To wit, he is using/abusing a clause in our contracts that states we must be 'fully fit to work at all times' to send engineers home, without pay, if he considers them to be too tired to function effectively. This includes anything from having large bags under the eyes, to yawning, to putting one's head down on the desk to making what he considers 'stupid mistakes'. This happens at least once a week, usually more often, and he makes the rounds at the start of the evening meaning each team member loses about 10 hours of pay if judged unworthy.
Current Situation
There has already been a screaming row over this new tactic, which resulted in one of my team being placed on a final warning for insubordination, something I feel is totally unacceptable given the circumstances. I scheduled a meeting with the new manager along with the day team supervisor, where we explained that the new anti-tiredness tactic was having the opposite effect to that intended, only to be told to 'bugger off and stop exceeding [our] authority' in as many words. I communicated this to my team, who were not best pleased by the result, and now I'm not sure what approach to take. I can think of three:
Go over the manager's head and complain to the director of IT. This could backfire very badly on me if the director backs the manager and retaliates, however I think the executive team needs to know how things stand as the situation is escalating fast and will have a serious impact on business processes if it's allowed to continue.
Lodge a formal complaint(s) with HR about the behaviour of the manager, which is an approach my day team counterpart favours. She claims that the manager's behaviour could easily be construed as bullying, and his interpretation of the contract is not necessarily correct. These are good points, but I still regard this option as akin to nuclear war, with mutually assured destruction for all involved.
Confront the manager with what amounts to a vote of no confidence, signed by my team, myself and as many of the day team as possible. This is the approach favoured by my team, and while I like collective action and solidarity, I would almost certainly be fired on the spot for gross insubordination and have to win my job back on appeal, and I'm just not that selfless.
EDIT: Wow, thanks for the response folks, it's really been helpful! I've marked Peter's answer below as that was the approach I took, however a comment on the original question got it right: this was a prelude to a large round of layoffs in which team sizes were cut by around 1/3, and the company was employing dirty tactics to try to reduce their redundancy payouts. I'm currently seeking alternate employment for reasons that should be obvious. Thanks again!