Never owned or personally used a Boresnake. Never made sense to me, to keep pulling the dirt and all I wanted out - back in.
Clean patch each time, and only going one direction - makes sense to me. This is how I was taught.
Rods were used most times, even a 3 pc GI rod, with Muzzle guard taken afield by one of us, in case a shotgun wad got stuck, or squib load, or mud in barrel.
Before the Otis kits, Mentors made me a pull thru made of Rawhide lace. Clean patch each time, going one direction only with a pc of straw to protect muzzle, small glass bottle of oil that all fit in empty shoe polish tin.
Out in rain, snow, or coming inside from cold to "mud room" or "cold room" and not wanting condensation to occur in barrel , run a oiled patch from breech to muzzle.
Not trying to "clean" , instead remove moisture, and hold. Not a tight patch, and run another "not so tight" to remove anything that came out before shooting again.
I rarely clean a barrel anyway, I concern myself with chambers, extraction and feeding.
Just me, just feel too much time spent on what is not important and not enough on what is.
Seen pristine bores, and chambers so gritty with plasticized residue, the shotgun would not feed or extract. Seen extractors break from this, and have had to use a brass hull "knocker outer" or wooden dowel to get that hull out ...
you could have eaten off the bore it was so clean though.