try jfk-nrt in Y on AA. Fees only £29.20. Good availability, and you could redeem it for a 'friend'. A good $1000 worth of flight, and 50,000 miles for this is a very fair rate considering the UK equivalent, LHR-SIN would cost 80,000 miles.....
There are other US options (redeem on AA, not JAL or CX):
ord, dfw, lax - nrt
ord - pvg
ord - pek (from may)
ord - del
The other option is LAN.
MAD-LCL is only 27.20 in taxes (250 on Iberia), but you don't have enough miles and would need to position at MAD, so it won't be worth it.
Consequently, you might be better off redeeming for two Y, or one J, redemption within S America. 25/50k miles, and minimal taxes. If you can find SCL-IPC availability, that would probably be best......
http://www.lan.com/info_viajes/clase...ess-en-un.html - full flat bed, 74" seat pitch, 15.4" TVs - looks like a great deal to me.