Naah, part of the game is bag management, and deciding when to play. You said you wanted the grey items to have "meaning" part of that meaning is the balance of value of possible reward versus the inherent value of a bag slot. A casino betting thing would work too. But basically that's no different from vendoring in the end, you don't "do" something with the greys, and betting is only fun if you lose something of value from "losing." Another thing they could do is group stacks of greys based on "item shape" in that you'd take up less room in your inventory with them, but still have to manage inventory space. It'd probably become something you got used to doing every time you're in town (like you vendor them now).