We ordered a carbon monoxide detector through ebay from China, installed it (well, put it on the cushion…) and fired up the POD kerosene heater and kept it running at full blast for an hour. The detector showed nothing. Then we hung it at the anti down draught contraption on the chimney. After some 10-15 minutes it showed 118 ppm.
So, obviously, some exhaust fumes are getting into the cabin although not sufficient to pose a serious problem, it seems. A different exhaust solution (another chimney cowl or a fan to force exhaust gases out) might keep us sleeping more soundly. More testing needs to be done.