Another member of the club here...
I can't afford to fly premium class most of the time, and do manage to take night flights (with Ambien) but otherwise use many of the same tricks. TATL flights tend to be chilly (and even chillier if you're in an emergency exit row, which I usually am), so it's not typically an issue unless you're stuck on the ground.
If you are, here's what helps me:
1. Dress in such a way that you can strip down to just about nothing if absolutely necessary. It's knowing that I can do it that's the most help, frankly---I've never had to get down to my bra and panties on a plane. Non-binding clothing very helpful.
2. Have a bottle of water and a wet towel at your disposal. Using the wet towl for your forehead and neck will cool you immediately, particularly if you fan yourself.
3. Talk about it. You may or may not already have figured this out, but talking about your claustrophobia, either with the stranger sitting next to you, or with the FA, can immediately improve the situation. Not only does it distract you but it somehow makes it all seem much less like a big deal. I used to try and avoid thinking or talking about my triggers, but now find that doing so is very helpful.
4. Keep your bladder empty. Pee the very instant you think might need to, because if the seatbelt sign goes on five minutes later your bladder may contribute to your sense of entrapment.