Tipi tents are a sheepherder tradition, but they lack decent living space. The stand-up area is close to the stove and the rest of the space is pretty confined for adults. Nylon or any other synthetic fabric is a bad combination with a stove: you'll get zillions of pinholes in the roof from cinders, and a scary meltdown is not uncommon.
If you want a heating stove, get a canvas tent.
Having lived for extended periods in various tents with box stoves, my favorite is the Kirkham's Springbar design.
Springbar Tent Models
These tents are used a lot by backcountry and river outfitters, which is how I got to know them. I've got an 8 x 10' model with standup room (I'm 6'4") for the entire floor area.
The back of the tent has a full-width screened window. Mine has a pitchout flap over the door. I had the floor fitted with a zipper, so the stove can sit on the ground, and a fireproof stovepipe panel sewn into the roof. The canvas is rather light and the size and weight of the tent compares favorably with a bundle of canopy and sidepanels.
They're extremely livable, with big, tough zippers, bug netting, windows for ventilation, and pitch-out awnings for nasty weather. They also have modular options for larger groups.
The prices haven't increased all that much since I bought mine, many years ago. Great value for the money.