If it’s a big company then keep your ear to the ground, find out if there’s another team or department you’d like to work in, and talk about it with your manager. Be patient. Big companies have a lot of benefits and it might be worth waiting for a position to open up.
If you really want to work somewhere else then apply outside of work hours, don’t just quit. It’s easier to find a job when you already have one.
I don’t think reshipping in itself is illegal. If you’re buying something illegal in the final country, sure, but there’s a lot of stores that only ship to some countries even though there’s no restrictions on the actual goods.