The close reasons need to be updated to include the new website.
Going forward, how will this be handled when we have hundreds of sites? I don't want to deal with a drop down that has more than a few possibilities...
How so? the site hasn't proven it will survive private or public beta thresholds.
So, at best, this is premature.
edit: we do have new question migration paths but I don't think webapps is a valid path from Stack Overflow -- unless you can cite more than a trickle of closed questions that belonged there.
The correct current answer is to mark it for closure as off topic.
If you feel kind, point to the correct other place to ask the question. I agree though, more than 3 or 4 places to vote to move something is going to turn me off from voting to move things there. I liked the idea that came up elsewhere of requiring some level of rep on the target system before you could initiate a vote to move a question there.