Your sketch shows a nice clean, simple system and
should work just fine. An 8" J-tube (equal to 20cm) can handle up to 45-50 feet of straight duct even without a really good chimney, so 10m (33') of straight duct with 5m (16') of chimney, half inside the space, is likely to actually run hotter and stronger than ideal. I believe based on my and others' experience that you could use a 6" or 15cm insulated chimney which would be distinctly less expensive.
I have an 8" J-tube in a masonry bell, with a temporary 6" stovepipe running up 7' and out the sidewall, then up 9' to above the roof with 6" insulated chimney (so fairly similar to your proposal). It draws well in all conditions, and I still need to partially cover the
feed to avoid too much airflow through the system.
The only time you might have an issue with draft would be when it is warmer outside than in with a stone cold system. Then you might need to prime the chimney with a small fire or other heat at the base of the chimney. A bypass or reheater from the chimney being close to the barrel would not help much in that case anyway.
By the way, you don't need the insulated chimney all the way up inside the building, only within about a half meter of the ceiling (your
local building code may be slightly different) and above the roof.