Got the same situation here. I have a M series of swagelok (non vernier), and take about 1/4 turn to have enough flow to supply CO2 for my 120g tank. After that point, CO2 flow is way to much. Working pressure is around 20 PSI/1.5 BAR.
Using 1/4 of 10 turns with the M series, then you have too less resolution (to my opinion) around that 1/4 turn. That's why I'm using working pressure for fine adjustment / tuning! Bit the other way around than it's supposed, but it's working nicely.
Next time, I would buy a S series: as it take (0.030/0.0040) 7.5 times more turns for the same output. That would bring you to about 4 turns out of 10 as LeftC already stated. And it would give you 7.5 more resolution at 4 turns!
I can imagine that it you have a non return valve with a lot of backpressure, it would require more pressure and more turns so to say, but then I would cranck up the working pressure. My reg goes to 150 PSI more than I'll ever need.