I'd skip the soy milk and other similar "remedies". First step, go to CVS and buy yourself a three month supply of minoxidil - use it twice each day. It's very cheap, available in the hair care section, and the generic is just fine. More importantly, it actually has been clinically proven to work.
Second step, get your doc to put you on finasteride. Again, it's easy, very cheap (if you use the generic and cut the pills), and it also has been clinically proven.
Both are probably cheaper than the quantities of soy milk you're describing, and probably far healthier too.
Your hair is important, and thinning hair is a nightmare to get back. I strongly urge you to skip the natural remedies and go straight to the things that really do work, because you'll end up losing even more hair while waiting for the soy milk to have an effect.