I forgot to mention - one long-haul positioning option also worth looking into is LHR-ICN on BA, then connecting to HND using JL, a genuine short hop (2 hour flight) for 7500 Avios in Y. (For availability you can also look into JL from Seoul's secondary airport, GMP, to HND, though I have zero idea about the logistics of an ICN-HND transfer!)
Apparently JL killed their earlier NRT-ICN route because they couldn't compete with LCC flights costing peanuts, so that may be worth exploring.