Given the lack of award space on my dates, I actually think what I will do is book coach.
By tagging on a flight LIM-LPB (ITA Matrix is great for finding city pairs) and thus turning my one-way flight into an OJ, I can cut the fare in half.

A status match from BA Gold to LANPass Black should give me and my gf complimentary upgrades. I would still have preferred to book for miles, but beggars can't be choosers, I guess.