The most valuable hack I've discovered and used when dealing with the health system (and bear in mind this is in the UK, where the main problem is not cost, but time) is to be great friends with a GP. I always discuss health issues with him before going to the doc, so there are no surprises afterwards, and I know exactly what to say to expedite the process.
It turns out that there are various magic phrases you can use to speed up the outcome, guarantee a referral, etc. If you're friends with a doctor, they'll tell you those phrases.
It probably won't help with all the waste in the process, though. And it definitely won't help with closed hardware.