Green compound won't likely be very effective on S30V; it's not aggressive enough to effectively abrade the vanadium carbides in that steel, but it will still abrade the basic steel in the surrounding matrix. End result is, edges tend to become rounder/blunter as the matrix steel (iron + carbon) abrades away, exposing the much, much harder and blunter carbides. Diamond compound works best for steels like this, because it's much more effective at abrading and shaping the carbides to a crisp & sharp edge. Obviously, this can also be done on the hones (diamond), and the better the work is there, the less additional work is needed on the strops. Focus on getting the edge as pure as you can on the hones, and the rest will be much easier.
On 8Cr13MoV, green should do OK, assuming the edge is ready off the stones. Very similar to AUS-8 steel in makeup, and not too much carbide content. On this steel, I'd more likely prefer using aluminum oxide compound (most often 'white', but may also be pink/blue/grey) or silicon carbide (black or very dark grey). Either of these is a little more aggressive on higher-alloy stainless (chromium carbide content). BUT, if the edge is really in good condition off the stones, the green compound will still work well. Otherwise, it may take a little more time, and may tend to round off an edge instead.
Factors which will more greatly affect shaving sharpness, even more-so than the stropping compound:
- Edge angle: 30° inclusive or less will make a big difference.
- Full apex of the edge: If the edge isn't fully apexed off the stones, stropping usually won't help get it there.
- Obviously, inconsistent angle control or too-heavy pressure on a soft(ish) strop, like leather, can be counter-productive, especially as the edge becomes finer. Only takes an errant stroke or two to round off or blunt the edge, if the edge is very fine and 'almost there'.
If the above-listed factors are adequately taken care of, stropping to shaving sharpness gets a whole lot easier. When an edge is done right, stropping should only take a handful of passes to really make an edge pop.
David