Our Amsterdam location was unavailable for a short period of time but right now we have plenty of capacity and can easily now add capacity as necessary. You should see an option to order hosting in that location.
For the actual migration it's typically best you disable features that there is user input as information will get out of sync. What users typically do is order hosting and then disable their forums, forms etc. and ask for our team to migrate the site. Once our team has migrated the site the user enables the features again on our systems. Then any new data is only added to our systems. Along with that if your host uses cPanel we can migrate accounts in just a few hours typically (unless the host is slow or blocks backups). So you don't even need to worry about domain changes if you don't want to.
Your sites sound fine in a shared environment so you shouldn't need to worry about that aspect. They'll be very fast on our servers, I have no doubt about that.