Going on garden leave is an opportunity and a benefit for the employee to be released to seek new employment, it isn't a bad thing. For whatever reason they've decided you aren't in their plans so they're exercising their contractual obligation by keeping to the notice period.
In answer to your question, the employee's 'tool' is that of clever negotiation, so both sides come away with a benefit.
Eg, You could try negotiating a shorter notice period, as a 'tool' on your side of the contract, which would be better achieved by giving them a time-boxed plan of exactly what you commit to achieving and by when, rather than being resentful and begrudging, which could cause them to cling on to you longer than if you maintain some goodwill. So you could send your manager an email stating you'll (for example):
- Provide x hours per day/week of handover training to x staff (name them), including an opportunity for feedback from the staff to indicate they're happy with the training provided;
- Provide the team with a User guide/business process stored in xyz location - if this is already available, state this, as it's one less thing to do;
- Support for ad hoc queries throughout the weeks you are in post.
you could estimate the above as being achievable in, say, 6 weeks total, which is half what your contractual notice period is, a win for both you and your employer. As you mentioned you don't "need" the cash, so leaving early won't be a problem to you and they save on 6 weeks' pay. Notice periods can be excessively long (sometimes for no real benefit) and there's no harm in asking for earlier release if you have a viable exit strategy.
I'm going to be controversial here, but if you're as good as you say you are on this thread (I'm not doubting you, just saying), the above will be a breeze and you could be out the door a lot sooner, with good will and professional reputation intact.
As I said upthread you could go rogue and breach your contract earlier than agreed with your employer, but I would never recommend anyone does that. It could tarnish your reputation, which is difficult to recover from if you care about your career.
ACAS advice will be limited to your employment rights in law, which I expect will amount to some variation of what I've suggested (I.e. negotiate an earlier release). They could also say "you could just walk away and leave them to it, they probably won't sue" fair enough, but that would be an opinion and a risk, and not necessarily a wise thing to do.
I hope you get what you want from a bad situation.