Don't let the wait deter you. If you do need the machine, it can really improve your life.
Most of us wait because the prioritisation is by clinical need, and is usually 'good enough' and some because they can't afford it.
And I think if you have private insurance (i.e: double paying), you'll probably be paying more than the average American. I don't know for sure though.
You also have to factor in the (very large) public expenditure on healthcare in the USA. Americans also pay for part of their healthcare through taxes.
On top of that UK private insurance is much cheaper because it is 'top up' - you're usually expected to see NHS GP's first etc. and use NHS emergency rooms.
As such while it is possible to end up paying more if you're very high income, very few people in the UK will pay more even with private insurance.
So I took the test and got the results 2 days later and saw the specialist. He showed me the full scan said it's all clear. He then asked if I had insurance. I said no... he walked me to the billing desk and said no charge. What a legend.
Turns out chest pains was from GERD.
Here in Croatia, I could wait a couple of months or I could pay around $300 to have it done privately.