Goldpeak, I am doubtful that a doppler can diagnose venous leakage. I was diagnosed with venous leakage in the mid-1980s, after papaverine injections failed to produce much result. My symptoms sound exactly like yours.
The diagnosis was started with overnight monitoring of night erections, then the scan (which found nothing wrong), but got much more complicated, involving arterial and venous blood pressure measurements, some with isotope traces, followed by a saline solution pressure induced erection, which occurred at a pressure which indicated the problem. I had a venous resection of the third vein, and there followed 5 or 6 years of normal erections, after which the hydraulics reverted and the problem returned. This is all very old fashioned nowadays.
The latest that I understand is that "venous leakage" is a medical misnomer. The instances of an actual abnormal vein are very rare. "Venous leakage" symptoms are a result of soft tissue disease - the tissue doesn't relax or dilate sufficiently to start the process. That is why you get the "soft" erection, and no more. That is also why the surgical resection of the vein doesn't work in the long run. All you are doing is putting a turbo charger on a dud engine - works for a while, but not a solution. There is a really good description of venous leakage on the site somewhere.
I simply used VED
and the compression ring. After a while I found that I could get a half erection sufficient to pop a ring over, and manually massage blood into the penis from the base, so seldom used the VED. Using the ring has been accused of causing the sort of micro injuries that result in Peyronies Disease if you are prone to it, which I am. I also have Dupuytren's disease, and 10% of those sufferers will get Peyronies Disease. I have lately found the prostaglandin injections are working, but time will tell.
Perhaps you need to be quite assertive with getting advice and make sure you are happy with what you are being told.
But there is a solution that will suit you, and if you keep looking, you will find it. All the best.