Firstly, let's distinguish new LiveWire from old LiveWire: as I understand it, the former is a new privately-operated team, and the latter is an old, defunct school-operated team. Organizationally, people moved from old to new, but there's no common corporate lineage. Is that correct?
Also, let's get this out of the way: you make reference to differences of opinion between old LiveWire and HayWire. Are those cordial differences of opinion, or are you actually mutually resentful of the other team's methods? It's relevant for many reasons, not the least of which being that perhaps the school district was trying to kill some sort of rivalry that it didn't like.
Was the team's equipment
actually school district property? (For example, paid for with school funds, or donated to the school explicitly, perhaps in writing.) Or was it not clearly theirs to take away? (For example, bought by mentors or parents out of their own personal funds, and given to the school on the condition,
1 perhaps in writing, that it be used for 3456.) If and only if it's not the school's property free and clear, there may be a nuclear option available: you could sue them for
conversion, or rather, provide a strongly-worded letter suggesting you might do just that.
2 If you can honestly say that it appears to be an instance of official corruption, or deliberate malfeasance, talk with the other mentors about making some discreet inquiries in this direction. But if the school really does own the property, that effort will fail.
There are also plenty of political remedies available, but they may come with political consequences for the teachers who are trying to maintain their day jobs. Assuming the school board holds public meetings with an opportunity for open comment, I'm sure they'll enjoy having to withstand direct criticism at their next meeting. And doubly so during the next election cycle. If, in the big picture, it makes more sense to break the board's resolve, then this might be worth discussing. I'm not always a fan of political theatrics, but they have their place.
But beware: it's not unlikely that accepting the school district's decision ends up being the most beneficial solution once their expected perpetual intransigence is taken into account. Maybe you're in the best position already—moving on.
1 An "onerous gift" is one that comes with strings explicitly attached. If you accept the gift, you accept the conditions.
2 There's actually another option—the blow up the Sun option: you could file criminal charges. Don't do this. Given the description you've supplied, it's kind of cruel, not remotely worth it, and you'll almost certainly fail.