My only suggestion then is use Expedia or somesuch to find the earliest start from London with the shortest stopover. Should be able to leave Heathrow at 9.00 and be in the Hertz compound on Pena Boulevard by about 4.30.
JFK is out because to go to Denver you need to get over to La Guardia.
Via Chicago or Dulles is probably the best bet maybe go via one and back via the other to minimise the stopover times and hanging around in the middle of the night on the way home.
I always check the cost on Expedia and then check that with the airline's own web sites.
Currently I'm ex Doha so get a nonstop DOH-IAD with Qatar then a DEN on United. Back is via LGA and JFK-DOH with a 4 days stopover in the big apple.