Wirelessly posted (BlackBerry8530/5.0.0.601 Profile/MIDP-2.1 Configuration/CLDC-1.1 VendorID/417)
Keep in mind that AA international awards permit a free stopover at the North American gateway. So, assuming that aa.com shows "MileSAAver" award availability on the desired dates of travel, LHR-NYC (stopover) - ORD/DFW (connection) - DEN will cost the same 20,000 AAdvantage miles as LHR-NYC alone. Note that to get the stopover at NYC, one must fly there on a direct flight from Europe; if you have to connect somewhere in the U.S. first, then NYC would not be your North American gateway, and you would not get a free stopover there. Also, for the NYC-DEN portion of the trip, you can depart from JFK or from any of its co-terminals, which include LGA, EWR, and HPN.
You can check award-seat availability for the whole trip on aa.com by clicking the "Redeem AAdvantage Miles" box, and selecting the Multi-City option. For the first leg, enter "LHR-JFK"; for the second leg, enter "NYC-DEN."
Good luck!