From wiktionary: Verb migrate (third-person singular simple present migrates, present participle migrating, simple past and past participle migrated)
(intransitive) To change habitations across a border; to move from one country or political region to another. To escape persecution, they migrated to a neutral country.
This is already common usage and I don’t see the need for any prefixes to the word. The Etymonline definition is giving the definition of the root, not the current english word.
The problem we’re addressing is that the prefixes are made redundant by the syntax of to and from. ‘immigrating to europe’ ‘emmigrating from europe’. Dropping the prefix in this context doesn’t change the meaning: ‘migrating to europe’ ‘migrating from europe’.