Sam,

Last time I checked, Lufthansa offers service from FRA-BOG-LIM. The flight is offered 3x a week, I believe. It's a loooong flight, but would allow you to sleep better since you wouldn't have to switch planes in the US.

A better way to get to Peru using 1W would be to fly BA/AA LGW-DFW and then AA DFW-LIM. The LIM-DFW flights leave around midnight and are about 7 hours long as compared to the 5.5 hour from MIA. You could also do BA/AA LHR-LAX and then LanChile LAX-LIM. This would be one hellish trip, however. LanChile also serves LIM from JFK.