The gas system screw has a spring inside, so pushing into the barrel as you turn should keep it from jamming....
It has been my experience that "flyers" and "stringing" are caused when the rifle is out of tune.
Lots of folks say if it's scoped the barrel timing shouldn't be an issue, but it has been my experience that it can be a big factor when trying to shrink groups.
Whenever a new to me, or a customers, rifle hits my bench the very first thing I do is blow the rifle completely apart until a barrelled action is sitting on my bench. then I double and triple check every single thing for alignment as I re-assemble.
Usually I find the biggest culprits to large groups and fliers/stringing are (in order)
1) Op-rod alignment (loose op-rod guide)
2) flash hider; even USGI FH are not all perfect.
3) bolt lug contact
4) barrel timing
If any of those 4 things are wonky, you will have wonky groups. If those 4 things are ruled out, then it's time to start digging a little deeper. Check your gas nut, piston and gas cylinder lock if they are too tight or too loose you'll have problems. If the barrel is even 2 degrees out of TDC then you will see largish groups and stringing.
In regards to the black feather, I don't have a lot of experience with them. I've installed quite a few rifles, but I just don't have the trigger time to really form a good troubleshooting guide. But from what I have read, the barrel tension is a pretty big deal..... Frank at M14,ca has quite a few exhaustive post about this at the m14 forums.
I have also found that Federal blue box 150 gr ammo is a very good barometer of how the rifle will shoot. It is the ammo I test all of my customers rifles with before calling a rifle "done".
Above all else, remember some rifles are just poor "groupers" but are still good shooters.... I have a SAI that went from a 7" rifle to a 2.5" rifle just by tuning (and a few aftermarket parts). I believe that the SAI has a poor barrel because it should be a solid 1.5" gun what with what I've done to it...... But I can still hit a pop can at 100y off hand with boring regularity.
Cheers! and welcome to the addiction!