I (we) can't give you advice that counters that of your doctors, but I can say a heart mummer condition is rather common (I don't have the percent of population, may be able to find that on the web by age), even in the young.
From what you say, it "sounds" to me like anxiety and other non-heart driven problems may be driving your symptoms.
If it were me (that would be 55 years ago) I would probably try to get through the exams and see how I'm doing. In fact 55 years ago I suspect a echocardiogram probably wasn't yet invented... and, yes, I do recall being told along the way (I very rarely saw a doctor) that I had a mummer or other heart abnormalities. Eventually, at about age 55 I did come down with a real heart problem, atrial fibrillation, which is not, I believe related directly to any mummer condition I may have had.
We in the USA are on the path to were you seem to be now: public health care (which isn't free - we all pay) supplemented with high cost private if we can afford it or just can't wait. $US 780 is more than what the procedure cost here best I can recall. When seeking private practice help it may pay to shop around - here in the USA it is sometimes possible to get lower cost care in a "clinic" environment. I don't know the exchange rate US$ to NZ$, that could be part of the "cost" difference when we speak "dollars".
Sorry I couldn't be of more help, maybe my post will get some more helpful responses flowing. I hope you can focus on yoru studies and tests, that is important too and it will move your mind off the subject of health symptoms.
I just got my bill for my echocardiogram done a few months back. The Medicare plus my portion cost was $430.95. This reflects a Medicare approved charge scale, and doctor do not have to accept that amount. My currently do, but the future doesn't bode well on that point. I need to do a little more research to determine if there were other costs, e.g., doctor charges applied separately.
Sorry again I can't provide more help, but getting the bill caused me to recall that I had commented on what a private practice charge is in New Zealand relative to my recollection of charges in the USA. Again, I am covered under government insurance due to my age, but that isn't "Free" either, not even to the old folks, I have to pay 20% of the approved amount, plus I pay a monthly premium and I paid into the program via payroll deductions since the inception of Medicare program approximately 40 years ago.
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It's interesting to see the differences in costs of ECHOs. I had a standard ECHO last month since it had been about 2.5-3 years since the last. My insurance was billed $3,345 for it and luckily paid it all and I wasn't responsible for any of it. The amount they billed my insurance seems absurd compared to the two costs previously quoted.
There in lies the secrete of Medicare (government health management), it sets the allowed costs very low. Now this helps the insured who still has to pay a co-pay of 20%, but 20% of a much lower amount. As I recall the bill was over $2,000, but the allowed was as stated above. This was true to a lesser extent when I was on private insurance, United Health Care is still my secondary coverage, the large insurance companies also had lower "contract" rates for most procedures.
Now the "rub", when the allowed rate gets too low, doctors quite accepting patients, and the few doctors who do have long waiting lines - witness the originator of this thread... hope he gets at least something of value out of the follow up.