Welcome to FT addio.
By my calculations, the 'cheapest' free ticket you could get UK-GIG would be 80k miles in off peak times...That would be 2 40k awards, one for UK-USA and the other USA-GIG. And it would have to be during the period Oct. 15 - Nov. 30 or Mar. 1 - May 15, when the off peak award periods are the same.
If you picked up an extra ~4k miles to get you to 40k, you could get halfway on miles. For example, purchase a UK-USA ticket in November when the fares are cheaper, then use your 40k miles for an award ticket USA-GIG.
That's about the only thing I can come up with.