Are you aware that there are trains (not the Tube) called the "Heathrow Express" to and from Heathrow and Paddington? These are trains dedicated to that route and those passengers. They leave every 15 minutes from their own platform, which is at the same level as the trains' floors, so no heavy lifting. The service is 24/7. Each carriage has dedicated space at each end for your bags. You do not need to check bags and you can keep them in sight, so very secure. Paddington is a train station and has three Tube lines as well, so you can get from Paddington Tube Station to King's Cross on the Circle Line without changing Tube lines. You should reserve your seats on the Heathrow Express website; there are two classes. I seem to recall they recommend making your reservations early and you might get a discount if you reserve online, idk.
There's tons of stuff to look at at Paddington, plus lots of shops, including a Boots, a WH Smith, even a Marks & Spencer. Don't pack your toothpaste in your bag; just buy it there. (Also applicable at Heathrow, I expect.) Lots of walking space to stretch your legs (whew!). Recommend scooping up one of their baggage trolleys if you can, but you will need some British coinage, I think maybe the one pound coin.
I have done that Tube trip with two family members, six suitcases, three backpacks, etc. etc. Carriage was packed, so stood all the way, (45 min?) except for the time I spent perched on my American Tourister, c. 1970. (Boy, do I miss that bag.) Still have the flashbacks....