Have you finished cleaning the hub internals and reassembling outside of the shell?
You will be able to simulate shifting on the bench this way. The lock nuts only need to be snugged up a bit. Drive the sprocket in the forward direction while holding the brake arm still. Both clutches should always turn with the sprocket going forward. You will be able to tell if the clutches are swapping which is in control when you kick the sprocket back enough and start turning forward again. One position/gear will have all 3 of the index spring tines set in the 3 recesses of the clutch. The other gear will have the 3 raised parts on the driver pulled up and stopped against the 3 tines of the index spring. This is what keeps that clutch disengaged from the hub shell and let's the other clutch take over control. If all of these things happen and the left clutch moves close to the left driver when in control it's shifting, reinstall the assembly into the clean hub and try it out. If it still slips that's when you jump to the conclusion that the hub shell is worn out.
If the hub only wants to stay in the one position/gear, start checking for broken coupling spring "windows" not allowing the hub to shift or possibly weak retarder springs. Then check for broken tines and pawls on the index spring and for wear on the inside of the driver that index spring mates to. Please post pictures of what you find and we can assist.
This guy's video makes for a good visual. Neither of us are using 100% correct terms, but this will help get you started in the right direction learning the theory of the hub and you can start asking the right questions once you've looked the hub over. Then it will be on to the parts diagram to properly identify the part you may need. Hope this helps!