Hi and thank you for your question.
I am confused, you stated up front the manual states 670ml. That is the fork capacity. If you have run the bike long enough to develop a fork seal leak, you should change the oil anyhow. I am not aware of any manufacturer that publishes a conversion from cc to oil height. As you stated, Yamaha does publish both for stock, but they are not going to tell you to put xx cc's in to raise the fork oil level 10mm.
The simplest solution is to drain the oil out, put 670cc (1cc=1ml) back in, collapse the forks, measure the distance to the oil from the top of the leg, then add fluid, subtract 10mm from the 670cc level measurement and suck out the excess down to the stock height - 10mm.
However, that being said, I think what you really need to achieve the damping you desire is to re-valve for mid-stroke. The bottoming can be addressed with compression. My next question is, what is your static sag with you on the bike, geared up?