I'm not exactly sure what you are wanting. Do you want to grey the timbers? I have tried the steel wool/vinegar/water method. I found I had to tape off a bunch of test sections on a board and thin out the mixture with more and more water until I got the finish light enough. I actually tried it on White oak, DF, Beech, and Cedar. The White oak was the worst. This mixture will turn the oak very dark and an un-natural look. Even thinning it out a lot it tends to still be too dark and look un-natural. It looked better on the other woods, but still not totally like natural greying. I also contacted Lifetime Wood Treatment and they said the same thing about Oak, that it would turn it too dark. Their product is a powder and I suspect that it is very similar to the vinegar/steel wool mixture.
In the end you just need to experiment.