I worked my way through most of the cabin crew
I've tried many tricks over my various Oz-Europe flights. (Er, not for working my way though the crew, I'll leave that one for Ron...) Total duration Oz-Europe is usually a smidge under 24h although I've had one last 41. Most often any tricks have worked on one flight and then never again. The only really pleasant one I've had was one where I was upgraded on two of the three legs and on the third had a row to myself.
As Ron mentioned, you need to plan for the possibility of the night feeling chilly; you also need to know you'll have some kind of neck support. I've trained myself to zone out for most of the flight nowadays so I can just sit there with my eyes masked and ears plugged even if I'm not sleeping (especially if my ears are plugged with earphones (I use the kind which are basically earplugs with headphones in) and there's something relaxing playing of course).
Window seats are good for not being disturbed by people clambering over you, less good for getting out of without disturbing people. Alas if you drink lots of water (or of course booze, which is not usually recommended but sometimes it's helpful for zonking out) you will indeed need to get out of your seat now and again.
Anyway, 13 hours, that's only half a flight. You'll barely notice it.
Oo yes - if you're going to have to go through security a few times, don't wear a belt, put it in your suitcase (unless you need one to keep your trousers up of course). It's amazing how annoying having to take it off for the scans can become once you've done it a couple of times in a couple of hours.
Oops, sorry Ron, I added most of this after your next post!
One good thing about flying nowadays: the entertainment systems are often the sort of thing I could only have dreamt about when I started doing this sort of flight - I've had one with about 700 channels. There's a downside in that the technology does take away some of your foot space - but having bunches of games, lots of films you can start when you want to, all of that helps a lot. At best use some of those headphones I mentioned which are basically earplugs plus earpieces (like the Koss Plug or Spark plug - very cheap compared to electronic noise-cancellers) and get yourself an airplane adaptor beforehand.
Jet lag is another question of course... I still don't have a recipe. Except perhaps not to wuss out when you get there but do stuff - also be out in the sunlight (or at least the daylight!) as much as possible so your body gets the point. Last time I flew back to Melbourne I didn't have anything to do so took the odd nap - big mistake, it ended up taking ages to acclimatise.