Be offended, but take a step back and think about this setup. Don't let it kill you.
Every winter around here someone burns a house down with a setup like this, with very similar reasoning for why.
What happens when you fall asleep in front of that, the wall catches and then you wake up to the roof on fire? Can you get out quick enough?
In your case this doesn't appear to be primary heat for your house, so why risk it?
Not only all of this, but then there are people offering advice or suggestions that are just as bad, or worse.
Stuff like mixing different classifications of vent piping. Or external insulation on Type B vent pipe.
The OP needs to follow the manufacturer installation instructions and use UL listed materials and methods.
Type B double wall pipe is listed for use in an attic or a chase.
Triple wall vent is specific to the manufactured appliance that uses it, like a factory built wood burning fireplace (usually made of metal with a refractory lining). It is an engineered system. One cannot use Type B vent or Class A fuel burning chimney pipe on a metal box wood burning fireplace insert designed to use triple wall pipe.
I'd bet that if single wall pipe is allowed on your stove, it is intended to be used for just a few feet to tie into a masonry chimney (this would absolutely be detailed in the installation instructions). There are factory built Class A chimneys for stuff like commercial kitchen exhaust, boilers and other fuel burning appliances (ie: wood stove).
Draft readings and the use of a barometric damper or other means of draft control are likely covered in the installation/operation instructions. It isn't simply add vertical pipe until it's high enough.