Shorty Core Fireplace Insert

So I am moving into a new space. There is a big chimney that hosts two fireplaces. The fireplaces are side by side, facing rooms on opposite sides of a shared wall. The living room and dining room. The dining room fireplace hosts a woodstove insert. The living room hosts a pellet stove insert. The pellet stove functions. But I am curious if a shorty core or Walker core might fit instead.

The openings are 3' wide by 2' tall. I can't measure the depth right now. But there is another fireplce in the house that also has a 3'x2' opening. It is 23" deep. There is some more height inside. The hearth extends out almost a foot in front of the fireplace.

So I am thinking about putting some sort of shortened core in the fireplace, with a stove pipe down in the back to serve as the siphon of a bell. And probably a removable metal front to hold the door and serve for quicker heat. Most of the heat would be stored on the ample mass of the chimney. Do you guys think this is viable?

Pictures for reference. Most of the chimney structure is in the dining room.

Jeremy,

Fitting one firebox core or another is not a problem, the problem is how a pipe will transfer the heat to the mass?  Right surface area is needed for a given firebox to extract heat from the gases. Potentially you could build a wall that would separate the front chamber of the fireplace bell (if any) from the chimney flue. The gases would give the heat within this chamber and the colder ones would go down to the hole in this newly built wall and would go to the flue.
It's easy to write, but may be quite impossible to build, because of space constraints.
Would it be possible that you would remove the insert and take a picture of the inside, facing the camera up?