When you clean the barrel, pull the patch/brush from the chamber to the muzzle. That way the crud you are trying to remove goes out the end of the barrel rather than getting pushed back into the chamber and receiver.
At least it'll be quicker/easier to clean the chamber.
I haven't brushed a chamber in years. I just put the solvent on the patches and pull them through the chamber/barrel from the receiver towards the muzzle. I'll usually spin the patch around in the chamber a few times before pulling it to the muzzle with the cleaning rod.
I don't get tore up about coated/non-coated rods. I don't use jags (because I don't push anything through the barrel, from either end.
Pushing a jag/brush/patch & tip through the barrel means you put a compressive force on the rod - which causes it to bend and rub the lands as it passes through. The bore guide a lot of people recommend will not keep that rod from contacting the lands if you push brushes/patches through the barrel.
If you pull the brush/patch through the barrel from the chamber end towards the muzzle and do it slowly you put the rod in tension and it will stay straight and not contact the lands unless you pull it sideways and make it contact the lands.
This has worked for me for about 40 years or so.