"Sharpshooter" for your first AS is great! Took me 3 times to qualify Rifleman (Expert)....
You're right...the old army-style web sling, used correctly will help your groups immensely! They are available online, including through the Appleseed store:
www.appleseedinfo.org
I hope you're going back again, sounds like with a little work, you can earn that patch. I have some great 10ft dry-fire targets, to use in the house during the winter.....PM me with your email and I'll send you some. Dry-fire will REALLY HELP with the 6 steps to firing the shot, and NPOA. Get your breathing/trigger squeeze rhythm down...make sure you're SQUEEZING the trigger, HOLD IT BACK, reset and prepare for the next shot. Any other AS questions, just ask...I have LOTS of info!