I have shown a white horse for about 4 years, I have plenty of experience with shampoos.
I used Quic Silver, for grey and white horses and it works very well. Only leave it on for a couple of minutes or else it might stain your horse. < That has never happened to me though!
There is also a new brand called "Gallop" it comes in different formulas for different horses, and I heard it works very well. I used Cowboy Magic and it worked really well for me, I don't know why it didn't work too well for you.
If you are really desperate to make your horse white, there is a product that comes in a spray can, that is specially made to spray out certain colors, they come in colors like chestnut, black, and white. So the white would definitely work on your horse. I also read in an article in a horse magazine, I think it was Equus or Practical Horseman, it was Gem Twist (or a horse just like him) that talked about how they got their pure white horse perfectly white for all their big horse shows. If you could locate that article, that might be the best answer! Good luck! Luckily I don't ride a white horse competitively right now, and even if I did my horse trainers prepare my horses for shows before hand. :)
Be confident. Too many days are wasted comparing ourselves to others and wishing to be something we aren’t. Everybody has their own strengths and weaknesses, and it is only when you accept everything you are — and aren’t — that you will truly succeed