why it's better to fly west than east

I think I have solved one of the major mysteries of modern life - why it takes longer to get over jet lag if you fly east than if you fly west. Please, if you are one of that minority who suffer the converse problem, don't bother writing: you are freaks, should be in the zoo, and are lucky that you haven't been rounded up and shot as you are clearly a danger to society.
For the rest of us, going east is a pain. Even if we sleep on the plane, we almost certainly won't sleep the first night we land, and we will be liable to fall asleep at the most inconvenient moments for the next several days, depending on how far we have travelled.
The reason, I believe, is to do with our dream patterns. Under normal circumstances we fall asleep partly through tiredness and the need to rest our muscles, including our brain function. But, as part of the latter, we clearly need to dream. No one, including me, is sure why we dream, but it seems to have something to do with making sense of our most recent or most concerning experiences, even if it is expressed in the form of the bizarre fantasties played out in the dreams we become conscious of. Deprived of sleep and therefore dream time for a long period, we go crazy, making it an ideal non-violent punishment and/or torture.
Clearly we have the ability to postpone sleep/dream, either because our brain tells us to stay awake to meet a deadline or survive serious physical threats, or because we're enjoying ourselves at a social occasion.
What we find much harder to do, and this is where eastward jet lag comes in, is to make ourselves sleep/dream prematurely. We don't seem to be able to sleep if we are not tired, and we can't dream if our brain doesn't have enough material to work on since the last session. And we seem to need a fairly regular pattern: despite the occasional delayed sleep, we need to sleep at regular intervals and jet lag of more than four hours is enough to disrupt that, especially going east because our bodies seem to say that, even if we have managed to sleep on the plane, it still won't sanction the next sleep/dream 16 hours later, as normal. It seems to register that we have slipped in an early sleep and wants to revert to the pre-travel pattern. That is why it is better to stay awake through the first day after travelling, but that is much harder to do that than to stay awake a few hours after a westbound trip.
It would be nice to end this analysis with a logical conclusion in the form of a pat remedy, but I don't have one - at the moment. Maybe the answer lies in trying to sleep earlier and earlier before we take off for the eastbound journey, to build up at least some sleep debt. It seems to be a case where credit is bad for you.
Anyone got any better ideas?