Not sure if already covered in this thread but this fare creates some interesting opportunities for US based Exec Club members or as an add on to an Ex-EU to US TP run:
AA/G3: JFK to Santa Cruz de la Sierra, Bolivia from $1212
Best deal I could see was LAS-LAX-MIA-GRU-VVI roundtrip for 965 GBP (at current dire FX rates). LAX-MIA and MIA-GRU on lie flats. 640 TP. Not the easiest to search but all the info is in the link.
The thread refers similar prices from HNL but I could only see in the 1400 GBP range