Are home-made cardstock cards durable?
It is pretty common in other CCGs to play proxy cards. This is typically made up of a common card from the game being played, in a sleeve with a printed copy of the desired card, cut from plain paper and the same size as the other cards, placed in front of the proxy card.

You are correct to point out that the sleeves do make the cards, and subsequently the deck, thicker. I wouldn't bother with liner sleeves (the really thin ones). These are intended to protect cards placed into hard shells. I'd try to make it work with deck protector sleeves.