I know you said you want the one piece steel version, but Dewey sells a Brass version with attachable loop or jag. If you want to make sure they never inadvertently spin out, locktite it in. They are $7 each and IMHO Brass is much safer than steel for barrel cleaning.
.22 Caliber Brass Pistol Loop Rod – 9 Inches. Model# 9-LB | J Dewey Rods