Lots of advice! I've done these flights many times, and feel much the same as you do - takes me weeks to psych myself up for a long haul.
1. There is lots of advice both for and against pharmaceuticals. I was initially against them, but couldn't get any sleep and arriving in Africa that way can ruin the first few days of a hunt. My doctor prescribed Zolpidem (Ambien). Initially 10 mg but now 5 mg, and I find the 5 mg is plenty. I prefer the 'sub-lingual' variety. Works fast. I suggest, as many have, that you try it out first at home. It doesn't keep you out for as many hours as you might hope, but once you start waking up, the key is to stay lying down with eye shades on. You can extend the time asleep this way. As for grogginess on arrival, almost any trace has left your system in 8 hours. Contrary to some, I suggest you take it as soon as you hit cruising altitude. That way on a 12 hour flight, you're awake for the back end and all grogginess, if any, is out of your system by the time you land. As for side effects, if we focused on side effects, we'd never take any prescription medication. Yes, some people (very few, I think) do goofy things on it, but hey - you can use it as a legal defence! I also find it helps me hit the ground running after an 8 hour time change, and for the first few days, helps me sleep past the jet lag. Never lost a day of hunting since I started bringing it along.
2. If you do have a problem with approaching panic state after a long time, you can ask your doctor for Ativan. It works well and tends to have fewer side effects than Xanax, which you might reserve for full blown panic attacks (also lasts longer in your system).
3. Load some movies or TV shows on a tablet. I can get lots on mine, including entire seasons for various shows. It's great to have when you want to zone out. With the games and the Kindle app I've loaded, I have more books than I'll ever need, and more games than I can ever play. I also load up on my newspapers and crossword puzzles, also on the tablet. Lots of distraction.
4. Go easy on the food and really easy on the alcohol. Neither does you much good at 38,000 feet.
5. Eye shades, ear plugs, noise cancelling headphones, compression stockings and a pillow of your own. All should be in the carry on.
6. Walking from one end of a big jet to the other can be like navigating an obstacle course on inter-continental flights, but every once in a while, its necessary to keep the blood flowing to the legs.
Good luck. I hate flying so much that if it wasn't hunting at the other end, I'd stay home. But it's well worth it!