Is there a way to force Finder to attempt to move something from a read-only folder? Usually, if you hold down command while dragging a file (or folder), the Finder will move it rather than copying. This works if you want to quickly move something between volumes (the default is to copy.) However, if you're dragging from a folder you can't write to, command has no effect.

Is there a way to make the Finder always try to move something if you hold down command, or an equally fast way use the Finder to move an item out of a read-only folder?
No, this is an implicit feature of the permissions system. Moving a file out of a folder is effectively deleting it from that folder, which is a write operation, by the permission system's logic, hence it's forbidden if you don't have write permissions.

Read-only access is typically used in situations where users need to access files, but shouldn't be allowed to modify or delete any. Being allowed to move files (potentially to locations where other users couldn't access them) would break that paradigm.

If you want to move that file, you could do so from the Terminal, using sudo mv file destination (sudo means perform the command as the super-user, i.e. a user that has write permissions), or you can change the folder's permissions from the Get Info window (in the right-click menu, file menu, or press ⌘I).