Originally Posted by
britenbsas
Do you work for HEX? This is an unnecessarily complex routing which will probably take longer than sticking to TfL and costs a lot more

No, but if I had to get from LCY to LHR, this is the most comfortable route with luggage. The transfer at Canary Wharf is about escalators and no stairs. The transfer at Baker St is to walk across a platform. The transfer at Paddington is escalators and flat surfaces. HEX has always been a good experience for me.
Jubilee is fast and reliable where Picadilly is less so. Bakerloo can also be but it's only a few stops.
It costs more, but I disagree it would take longer and I am pretty sure it will be less stressful than the District/Picadilly line.