Help with migrating same domain to new hosting

Migrate Guru seems to be failing me in terms of helping me move my WP site from one host to another.

I’m going to the new site (DNS is now pointed there), installing MG, and getting a Key.

I then put the old host’s IP address for my site into my hosts file (because DNS is pointing to the new host and I have no other way to access the backend of the original site), install MG, put my email in and the migration Key that I got from the installation on my new host, and set it alight.

It appears that MG is doing its thing, but at the end, when I take the IP entry back out of my hosts file and go to the URL as hosted by my new host, I have nothing but a blank, stock WP installation.

I was worried about this.

Any advice? Am I doing something wrong here? How can I best use this for my purpose?

Thank you for your help!