In order to make extrinsic regeneration scale better, it acts as a multiplier to your natural regeneration rate. x2 is an option but may be too high; x1.5 might work better.

Another idea is to make it so that regeneration gets better the closer you are to dying of HP loss, formally: if current HP = X * maxHP, regeneration will heal you at a rate of (2 - x) times its normal rate.