First of all let me apologize for the 'above' disgruntled comments. That's what comes from having to sit 'behind the curtain' just once too often.
Secondly, in trying to answer your question, yes, sadly CO may be holding out K fares hoping to sell higher priced H fares and/or charge the upgrade fee. While it is not the answer to your question, CO often offers Z fares which are 'sale BF' fares to LGW--but they come in at slightly over $2,000--with no miles, or waitlist needed.
As for getting to the gate early, the only thing you can hope for is an operational upgrade. This occurs when coach is way oversold and they will move some passengers to BF. This happens rarely, so don't get your hopes up. The reason for the 72 hr rule (IMO) is CO had a problem with flyers making phantom reservations in BF, then cancelling at the last minute with the hope those seats would then be freed up for upgrades. Also CO would like to sell at full value ($7800) those seats to any last minute business travellers generally flying on their companies dime.
So unless you are extremely lucky and get an operational upgrade, or find a 'sale BF' fare you can live with, I'm not sure how else you'll be seated in those comfy BF seats.