Logan, the 1873 will benefit with a little bit of tolerance removal. Taking away the burrs, rough edges, and those things that make a lever action difficult, the biggest thing working against you is the hammer spring. With the Winchester on your shoulder, cycle it firmly but a little slow. Leave the hammer cocked and cycle it again. Big difference huh? Now if you could just smooth everything up and leave the hammer spring off life would be great. HAH!
If you reload settle on a primer brand. Preferably Federals. Take the stock off the rifle. There are two screws working with your hammer leaf spring. The one on the end, the one that threads through the leaf spring; back it off until almost flat with the top side of the leaf spring. Put some non-permanent lock tite on the screw and leaf spring.The middle screw will not (shouldn't be) be touching the leaf or not much. Put the stock back on. Start tightening that screw. Here I would have a couple of cases with primers only. Chamber one, cock and pull the trigger. Probably will not fire. Keep tightening until it fires. Give it another quarter of a turn and you have got it. Should be a big difference in cycling the action.
Same goes for a pump shotgun. The biggest thing to overcome is the hammer spring. When I tune a 97, I take the spring out and start to flatten it to a match a template. 'Course, a lot of guys simply do about the same thing as the rifle. They loosen the hammer spring screw.
Keep safe.