Changing at Canary Wharf is not such a good move: it's quite a walk between the DLR and tube (which are at entirely separate stations): there are lifts at both however. If you do go that way, I'd advise getting off the DLR at Heron Quays instead - it's slightly nearer to Canary Wharf tube station (lifts there too).
It's also a pretty mammoth walk, by tube standards, between the Jubilee and Piccadilly lines at Green Park. (A long tunnel, with white, Jubilee silver and Piccadilly blue tiles: when you start at the Piccadilly end the tiles are mostly blue, but silver takes over as you get closer to the Jubilee...which at least gives you some idea of how far you have left to go). There ARE lifts at the Jubilee end, but I'm not that there are at the Piccadilly end. Anyway,I always used to make a point of avoiding that change when I lived in London and had luggage (there was an easy and obvious alternative for my usual journey there).
And the District/Circle platforms at Paddington are not so close to the Heathrow ones there, either (some narrow passageways too)....
Of course making plans for weekend, and especially Sunday travel in London is difficult when one doesn't know exactly which lines are closed on a given date for engineering works (although this information should be available, somewhere, on the TfL website)...
Your 2nd route (Mudchute-Bank/Monument-Paddington) sounds much preferable to the first: you'd have two short flights of steps to go up between Monument and Bank, and an escalator, but nothing too challenging, hopefully.
Alternatively you could get the District line from Monument to Hammersmith, where there is a cross-platform interchange for the Piccadilly line to Heathrow. (Barons Court too). That would almost certainly work out as the most luggage-friendly route.