Maybe this can help you with the chamber issue...
Lever Action Chamber and Bore cleaning. Rifle (unloaded) secured in a vise or cleaning fixture and the lever all the way down/breech fully open (or bolt lacked to the rear).
Step 1. Use a Dewey coated rod so as not to harm the rifling as you rotate it to clean or brush the chamber. The rod needs to be at least 4 to 6 inches longer than your barrel. I get ready to position the best fitting felt wad assembled to the Dewey rod tip adapter (or chamber mop, or bore/chamber brush) (all available from Brownells) in the open breech and sometimes use a needle nose pliers to hold it steady and centered to the chamber/bore centerline during the end of the Step 2.
Step 2. Carefully insert the bare coated rod (keeping it centered so as not to harm the crown) through the muzzle and through to the breech area to engage what you will be holding in position there, and rotate the coated rod body extending in front of the muzzle clockwise with your fingers until it’s fully screwed into what you are (now) holding steady and centered in the breech area.
Step 3. Once secured, pull the rod towards the muzzle a bit so the wad, mop, or brush it is now fully in the chamber area. Then by rotating the coated rod body with your fingers, you can wipe/brush the chamber quite effectively. Correct size wads work particularly well in .357 or .44 Magnum chambers which have fired shorter .38 or .44 Special ammunition. I have also worked through a number of “looser to tighter” bore/chamber brushes to get the cleaning fit I think effective. What I mean here is that I have found that not all .38 or .44 caliber brushes are the same diameter.
When using wads or a mop, I don’t drip solvent on it until I have it assembled to the rod in the breech area so I can rotate it from the muzzle end as I drip solvent/oil for even distribution. This also keeps your fingers dry. Once rotated a bit for the cleaning level desired, pull out towards the muzzle keeping the rod centered at the crown. You might do this more than once so you clean the bore simultaneously.
I can then wipe the chamber/bore dry using a folded patch inserted through rod tip held in the breech, with the needle nose if necessary, using the same (bare rod through the muzzle) method as above. The best part of this procedure is that you are always pulling the fouling from the chamber/bore area out the muzzle.
I use this same basic chamber to muzzle procedure for M1’s, M14’s, Mini 14’s, etc., even .22’s
Once clean, use the same procedure to coat the chamber and bore with your favorite preservative oil.