Another thing i do, and advise in my Paper Patching Video is a Set of small Side cutters, these Hakko Micro cutters is what i use, and have them in my Video. These things are AWESOME! Look at the Reviews on them.

I can snip a Twisted Tail off Perfectly Flush to the Bullet Base, BUT that ends up making them basically the same as if you were to “Tuck” the Tail. The binder reinforcement rings that you mentioned would FIX this as well, I will DEFINITELY be trying these out