Alright guys, I think after this incredible amount of help that I've got it.

The oneworld ticket is amazing – I can't believe more people don't know about them/use them.

If www.geobytes.com is right about distances between cities, then JFK-LON-LCA-CAI-LON is 8202 miles and JFK-LON-CAI-LCA-CAI-LON (legal because I only go to CAI twice) is 8913 miles. Both routes, therefore, are under the 9,000 mile limit, and flying in J would cost me 80,000 miles a seat. I would just have to check with the girl whether she would prefer the nicer ride to LCA via CAI or the faster direct from LON.

You guys are really amazing – I thought this board was helpful BEFORE I posted a question. Thanks so much for taking the time to think through this and share the tricks. I'm not sure how I'll get together 160,000 miles before Christmas (which is when I should evidently book), but we'll see. Thanks again so much. I've really enjoyed the day.

Adam

P.S. Maybe they'll bump a couple of honey-mooners up on a couple of the legs