When I was about 25, I wanted to leave a rubbish lodging arrangement, and was 4 months away from a big relocation (still UK) as I was going to start a graduate trainee job with frequent placement moves.
My then boyfriend of 6 months said - move in with me!
And I did, and it was lovely. No pressure - we were two young people and is could move out as easily as I moved in.
Then I got my first placement and it was very unexpectedly local - we were both over the moon!
We didn't last, but it was a lovely relationship at the time.
I would see this as a MASSIVE alarm bell that he's just not that into you if I'm honest, sorry.
You're going to move to a country and he's not even saying "hey, stay a month?" Yet he'd let a friend.
6 months in is FINE to say he doesn't want to accidentally end up living together. But 6 months in you should be super keen on someone and happy to 'play house' with them, if you both know it's temporary.
He's said you can stay a week. Love, at 6 months in you should be able to go on a 2 week holiday with your boyfriend. He's suggesting less time than a flipping holiday!
I'm very curious about this happy coincidence of him living in NYC and you moving there. You must have the skills and right to work or good possibility for a visa if you're interviewing already. Would you still want to go if he dumped you tomorrow?
If you are going FOR him, and he knows that and wants that, it should be open house at his for a couple of months.
If your boyfriend won't treat you as well as a friend would, bin him.
I'm a real stand on your own type. But I think this screams that it's you that things you've unexpectedly found something serious - not him.