If the LHR stop over and the extra $$ for the LHR airport hotel doesn't work; I have found it easier to get sleep on AA116 out of JFK --> LHR (AA98 ORD --> LHR would probably also work). Both are the last flights out to LHR.
Usually, I eat dinner at the airport (even if in J) and try to sleep as best as possible on the flight. AA116 and AA98 arrive close to what time you may normally wake up. You are still tired the next day but better than the earlier flights.
My concerns about trying the day flight to LHR have always been:
1. not sleeping well the night before to make it to the airport so early for a 8am intl departure. (JFK in my case requires a little more buffer time for travel due to the unperdicable NYC traffic delays).
2. not being able to sleep once in LHR airport hotel since body clock thinks it is late afternoon.