I do this same thing with my video files... I just use the Rename Files from Properties.
The biggest problem, and one I've complained about a few times (but since it's summer and I'm busy not that enthusiastically), is that you cannot manually assign the [Removable] tag. If you could, it would solve all my problems. As it is, I have issues... The way I've been doing it is:
0. I mount all the removable drives as the same drive letter (S in my case). Most of my view schemes have a search that excludes those files from the view (Not Volume Name S). I don't like to use the IsMissing method because it's slow and because if a file REALLY goes missing I don't want it to vanish, I want to know about it.
1. I assign a custom tag ([ArchiveID]) to the files with the volume name of the drive I'm going to move the files to. I have some "all media" view schemes designed that show these files along with the rest of my media. These schemes have a pane with this custom field added, so I can filter in/out the drives I want to look at.
2. To move new files over, I first assign the [ArchiveID] tag. I browse around my library assigning this tag. I then use a view scheme that has these panes: [ArchiveID], and [Volume]. It's easy then to find all the files that I've "queued" to be moved, but which haven't been moved over to drive S. I connect the appropriate drive and use Rename Files from Properties to move them.
The biggest issue is when you have more than one drive assigned to drive S. When you have a bunch of files on drive#1, and a different set on drive#2. When you connect drive#2, the Auto Import Fix broken Links function will consider the files from drive#1 "deleted" and remove them from the library (because it can see the parent drive -- so they fail the "protect network files" test). If you could manually assign the files "removable" status, then this wouldn't be a problem! As is, you basically can't use the Fix Broken Links feature, which is a bummer.