"Moving costs" for anyone inside the US is sure to be less than $1000.
If I was doing YC for a summer, I wouldn't need to move. I could just fly there with a couple of suitcases and a laptop, but I'd need some way to cover my existing apartment rent. That's a pretty significant expense over 3 months. And I suspect YC is not looking for companies who see the experience just "doing YC for a summer."
1. Move
It's easier to do it in three steps:
1. "Do YC for a summer" 2. Secure more funding 3. Move