Ok so I've been thinking this over a bit, and the solution is easy:
Just take box B! And make a deal or shout out loud or whatever that if there is a million in Box B, then you will leave and not open box A!
If however you open Box B and there is nothing in it, then and only then open box A and get a thousand.
but what if he thinks leaving box B empty will ensure you will take both boxes then?
The only way (i think) to prove him wrong is open only box B, and it is empty.... Then leave box A
I guess if we don't take either and there is 1,000,000 in box B that would be evidence Omega was wrong if the contents were discovered but that is irrelevant.
Box B only
Either I get a million bucks or I am the first to prove it wrong