The regular award rate for business class US-Europe is 57,500 each way. Anything else is a special fare and could be any rate. That one day there may be availability at 65k and another at 78k is just dynamic pricing
Taxes will be greatly different on JFK-LHR vs LHR-JFK due to the different taxes
If I recall correctly, web specials cannot be changed - you would have to cancel and rebook at the rate applicable, so if you have 65k now and change to a flight that costs 78k, you would have to pay the difference