Haven't had personal experience but a colleague recently flew with a 20 month old and a 5 year old from Brissy to New York (via LA). I know they had a planned stop over of a few days in LA just to break the trip up to help tke kids acclimatise to the timezone, get over the first long flight before starting the second etc. So maybe stopping over in London overnight with another stopover somewhere in Asia might be a way of breaking it up a bit????? Also maybe a night time flight when your kids would normally be sleeping anyway??

She also spoke to the Dr to see if there was any medication that could help the girls sleep while flying.

She travelled with her DH but I think he's a pretty useless flyer and so she would have done much of the care of the girls on her own.

I'm sure there are other more experienced world travellers here that would have more experienced advice.

Good luck