I think I see the problem; With the pipe running horizontal and the stove lying on its back, your setup is not going to draft well enough to contain the ash dust when you open the door to load. And with the door opening is facing upward it is much easier for dust to escape.
Seriously, the only thing that come to mind is the most common reason for dust in the room--Not being careful enough when removing ash from the stove, or when loading (I know you said you are careful when loading.)
Weak draft makes it harder to remove ash cleanly, so I have a couple questions;
How tall is the stack, from the top of the stove to the top of the chimney? These stoves are a bit picky about draft, from my understanding. If you put several small, dry branches in the box and get them burning, can you get a roaring fire when you open the air all the way? (You never want a roaring fire in your stove for very long, at any time, BTW.)
Does the stove put off a lot of heat?
Any problem with smoke rolling out into the room if you were to open the door halfway through a full load, or are you just throwing a few splits in at a time instead of loading full?
What kind of wood are you burning? Does it pop sometimes when you have the door open? That could be stirring up dust which could then get into the room with weak draft.
Do you choose a time when draft is at its peak to empty ashes? That would be when the stove is hot, some coals still remaining, and the outside temp is cold.
Describe in detail your method of removing ash and getting it out of the house.
I have a grate in the floor of my stove so that ash falls directly into the pan when stirred with a poker. Does your stove have the same setup?
There should be a metal tag on the back of the stove with the model number on it. You might need a mirror to see it, with the stove that close to the wall.
Frankly, I would not even burn that stove until the clearance-to-combustibles requirements set forth in the manual by Jotul can be met.