The only shot you can use (other than lead) that will cause no damage to your barrels, when using only card wads, is bismuth. Every other no-tox out there contains tungsten (other than steel of course). No matter how "soft" the manufacturer claims the shot is, they contain powder tungsten which will be abrasive to all barrels if not protected by thick shot cups.
There is a big difference between how soft a pellet is, i.e. the degree it can be crushed, and it's abrasive qualities. That is a point the various tungsten shot makers leave out of their ads.
If you want to continue to load with the same wads, your only alternative is bismuth. However, if you want to keep costs down, you will have to start using/reloading light loads of steel shot, using new wads, powders..etc.