Originally Posted by
The_Diamond_Z
I would do something like:
DLR -> Canary Wharf -> Jubilee Line -> Baker St -> Bakerloo Line -> Paddington -> Heathrow Express or Connect. It looks more complex but it's all luggage friendly and no stair that I can think of. Canning town may be the same effort as Canary Wharf, but I've not had the pleasure.
If you buy Heathrow Express Tickets well in advance it can be as low as £14 pp.
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