Moving SQL to a hosted server I'm in the process of moving a large (7GB-9GB) database to a hosted server. the old server uses SQL 2008 R2 and the new one is using SQL 2016. I'm trying to find the best way to reduce the downtime for this migration. I've looked into mirroring and replications and don't think either really fits the situation. I'm hoping I'm wrong and there's something I can use that I'm just not looking at properly. 

Is it possible to set up a mirror or something in this manner and then once I drop the primary just disable it?

I have full access to both servers but may need to have firewall ports opened if needed.
For 7GB to 9GB of database, I would advise you to just use backup and restore strategy. This is the most simplest and effective way of migrating small database. I highly recommend you look at dbatools to help you automate your migration (it also migrate your objects like logins). The most important part of your migration is you practice your rollback and making sure application/users can still connect to your database after migration. Always test before you go live.