Importing an EDMX is planned but it's not a thing to do in a couple of days, so we can't help you on that front this week. BUT, our designer has a wide range of naming tools and other tools to get a reverse engineered model properly setup on a legacy database. The competing tools might have an import system (although I doubt they can deal with a lot of the EF edge cases), our reverse engineering tools might actually get you very far with a project started from the DB.
Importing an EDMX is done through 2 ways: either an XML conversion (though this is very hard to do) or a meta-data retrieval from a live context which has loaded a valid EDMX. This latter approach is easier, but still complicated. One of the core issues is the code part: an EDMX contains mappings between entity type and code classes, which is unique for EF. If these are different than the normally used 1:1 mapping, importing fails. Just a thing to remember when you're trying to import your edmx.