2 ply liners suck and filling around it is not a guarantee that the liner will not be touching the bricks unless spacers are used all the way down. It would be much better to install a pre-insulated liner or just insulate the outside of the liner with the wrap.
I don't understand why oval vs round would change anything as far as the crock goes. Either the crock needs work or it doesn't the shape of the liner doesn't matter.
Double wall liners suck.
You don't have enough room for proper pour in insulation in your chimney with a round liner.
So I need to learn the difference between them. So what do I want? Most people call the double wall liner "stainless".