I have a telescopic section above stove. Love it, but..... it does not offer support for upper sections. My install is stove, telescopic section and 4' of single wall, approximately. The next three 4' sections of double wall are supported by the ceiling support.
I've also found if I remove the catalytic element and clean top down, then vacuum stove, it works just as well. I have to remove the top 4' section of double wall to clean top down. The messy part is cleaning that top section when removed. Which is the most built up. But that's how I do it now.
Also, the stove pipe can connect vertically or horizontally, based on the orientation of the stove section on it's 45° mounting base. I'd question if my stove would support 12'-13' of double wall. Single wall probably.
Then there is consideration of roof access. Even if you clean the stove pipe from below the cap, or cap screen, may build up and need occasional service.
We also have small grand kids, some 2-5, which although very good listeners, can not be trusted near a fired up wood stove. They are simply too spontaneous. We do not burn the wood stove in the house when they come over. That may or may not be a design consideration for you. You could add a low wall section behind the stove.
Our kids grew up with wood heat, with only one incident. Our daughter spun around like a ballerina with her arms out and back handed the stove. Sounded like a steak hitting a hot grill. She cried for hours, and wore a full hand bandage for weeks. She was maybe six, going on seven.
Edit: If you have ceiling fans, say two, one pushing air down, one pulling air up, you will get good air mix regardless of where the stove is in the room.
