I did try beetroot about 15 years ago, under mildly scientific conditions: I set my bike on the turbo trainer, with an accurate speedometer on the rear wheel. I then did a session wearing my Polar heartrate monitor, of carefully timed duration at certain speeds, recording the heartrate regularly. I then drank large amounts of beetroot juice for two, or possibly three, weeks and then did the exact same session with the same conditions right down to the tyre pressure.
The results were pretty much identical; the same speed (and hence power) for the same heartrate. From memory it is the nitrate in beetroot that gives it the performance properties, but if you eat a lot of vegetables, (like I do), you will be getting a lot of nitrate any way so it's just expensive, purple, urine.
Following your post I spent last night trawling the internet, and I've got the exercises so will be trying it. I have no qualms about EPO if it's produced naturally, (it's a hormone), and as I veer ever closer towards a return to competitive cycling ... I need all the help I can get!