Make/ buy screens. I do it all the time, costs about ten bucks each, and they have kits to make them the perfect size. I have to use the old school metal screens b/c my cat rips right thru those nylon ones
This is one option, but for the time, hassle and cost, it's just as cheap and easier to buy some of these down at Home Depot and take them with you knowing you can most likely keep using them no matter what size the window is instead of leaving them behind as a sunk cost:
W B Marvin Adjustable Window Screens ($5.48-7.33)
We've used them in the past, the construction is solid, and the screening material is metal. If you keep everything tight enough putting them in when you open the windows, they sat reasonably solid enough that our cat rubbing against posed no threat of it falling out, either... and ours is probably at least 2-3 times the size of yours.
That said, you mentioned the words abroad, expat and cat. If you're staying in the US with this lifestyle, ignore this, otherwise... do keep in mind that international travel with a small furry loved one can be quite taxing due to quarantine restrictions. Like, you would probably just get your cat back in time for you to move again type of situations.
Rebel Spy had a rather long topic on this issue for himself and his wife a few months back, and there were some passionate responses made regarding the subject (I think you participated in the thread, in fact). It might be better to have a trusted loved one look after the kitty until you find out where you want to re-root yourselves and then go through the quarantine process once for everyone's sake, including the cat's.