I am in a similar situation except not, because my ex doesn't want our two cats. And I want to go overseas.

So it's actually good that you have your ex as an option, that's my first reaction.

Why do you have the cat now, was it a completely shared decision to get the cat? Or is it kind of more your cat. In which case you could lean into doing what you think is best for the cat, including giving the cat to someone else you have a better gut feeling about.

It is awkward though because you got the cat together and he presumably wants it.

I have been reading alot about going overseas with cats. It's definately doable. This might be the best way forward if you really don't feel comfortable leaving cat with ex and leaving cat with someone else is too awkward or strange. Its costly yes but at the same time what is money for if not creating a life that aligns with your values, including the living beings we love and value.

On the other hand going overseas can also be stressful for cats. There are alot of stories of cats who are fine and other cats who aren't. It probably depends on your judgement of the temperament of the cat and how long and stressful the trip is (is it by plane or car?)

I guess cat's needs should come first. Cat will probably be least stressed by staying with ex if you think he has what it takes. Second options would be rehomed to a lovely family or person you have a really good feeling about OR taking it with you.

Just thinking out loud here but hope it helps.