Ian, does your two hours to get out of Heathrow include going through border control (or immigration or whatever they call it, sorry I can't remember at the moment)? I'd like to think that the new egates mean the horrendous long waits there are a thing of the past - but I'd be cautious about that.
I absolutely agree that taking the Tube to Kings Cross and then walking from that Tube Station to the Kings Cross railway station, is the most direct way, and the cheapest, from Heathrow. I've done the Tube between LHR and London (Earl's Court station), with luggage. It works but there can be a lot of walking involved with all your luggage amid crowds of people, even if you manage to avoid flights of stairs. You could get lucky and hit a less crowded time.
One alternative that removes the "hauling luggage around on the Tube system" factor: take either the Heathrow Express [HEX] or the TfL train from Heathrow to Paddington. Same route, but the TfL train makes some stops along the way and is cheaper, although you can book HEX tix online 90 days in advance for £12 [less for a weekend], tickets are good anytime on the stated day. Then go straight from the train at Paddington to the taxi rank and grab a cab to Kings Cross. Costs more but you aren't wrangling luggage up/down any stairs or on long walks from Tube to train at Kings Cross.
Obviously the risk of booking advanced fare train tickets (other than the advance HEX tix) is that they are for a specific departure time and you can't change them. If you miss that train, your advance tickets are worthless and you have to buy new tickets - at the higher walkup fare. IIRC Laura from the RS office, who often posts here, has written that they don't encourage the purchase of advanced train tickets on the day of arrival by air, due to that risk of delay and loss of money.
The safer option in terms of not missing a pre-booked train departure because of flight/airport delays: get a room at a hotel right at St. Pancras/Kings Cross for the night of your arrival, then catch the train to York the next morning.
You seem to be seasoned and enthusiastic travelers, and I hope you have a wonderful trip!