Something that hasn't been mentioned is the Otis cable system.
They provide a brass tip for plugged bores, but IMO it isn't going to work as well as a solid rod. Maybe it would work for a few inches of snow, but I doubt pushing on a flexible cable is going to handle mud. The Otis system is designed to be
pulled.
Here's a link -
Otis cleaning kit
Otis makes a full line-up, from just the cables to full kits ($150).
Also, there is nothing that says you can't use a 6" Otis cable
with your sectional cleaning rod, so you can bend it out to insert a patch through the slot tip (or attach a brush) and then pull it through, breach to muzzle. I believe the threads on the couplings are standard 8-32 cleaning tool threads.
This would work for actions which can't be cleaned from the breach, like lever-actions and some semi-autos.
Dirt gets pulled toward the muzzle, rather than being forced back into the action, just like Otis recommends.
However, the cleaning rod sections are 7" long and don't fit in the cute little zipper pouches Otis sells...