I think currently the game treats them as different cards with separate stacks, as per pillars. This would probably make it replace the previous shield as though it were a different one, but the code could probably be changed to accommodate this shield. If so, I think the first one you played should decide how the stacks affect its DR.
I don't much like the upgraded formula. The majority of games, it will not get past 2 stacks, especially with PC around, so it's just more costly. I'd rather it start with 1 DR but increase by 2 each time, so the path goes 1, 3, 5, 7, 9, 11 instead, making it more useful than the unupped starting at the 2 stack point and justifying the cost without making it absurd past 4 stacks.