I second the idea of jumping on the tube/train into London. You'll get a return trip, decent meal, couple of drinks, and an hour or two of sightseeing for less than you'll pay to get into one of the (sub-par) third party lounges. Six hours is more than enough time. If you have a US passport then you can use the e-gates, so unless there's a problem you won't experience any delay passing through passport control.

Tube is cheapest but slowest (45-60 mins)
Heathrow Express is quickest but expensive (15-20 mins)
TfL rail is the in-between option (30-ish mins)