With the octave string there is an extra saddle piece that floats on top the regular string saddle.
How to adjust these? Just loosen and pry it forward, seems like brute force. Get the main string intonated then move to the octave and ...
You have the right idea except for the "brute force" prying. You might get away with adjusting saddles on a tunomatic when the strings are under tension, but even then I recommend against it. Much better, imo, to take all the tension off the string (or pair of strings when setting the main string intonation) before moving the saddle. Adjust the intonation of the main string first, as you suggested, since that adjustment affects both strings. Then work on the part that only affects the octave string.
I realize this might seem tedious, since you will have to repeatedly loosen, then retune the string. But it will cause less wear on the saddle.