This sounds like exactly the use case of Entity Framework. I am making a few assumptions here. First that when you make this statement:
"I have a domain model architecture in which my domain/business objects were created based on the problem domain and independent of any knowledge of the physical data model or persistence structures."
That you mean this domain was created in the EF designer? But then you say:
"However all of the fields that need to be persisted do exist somewhere or another within my domain model, but not necessarily in the shape that my auto generated .edmx POCO entities have them."
This sounds to me like my first assumption is incorrect.
Next, you dismiss code first? If your domain model/business objects are code based and you want to persist them to a relational database, that is exactly the use case for code first. You have the code, now you need to create your DbContext and map it to your physical model.
However you dismiss that... so some thoughts:
If you have a domain model of code based business objects and you have an EDMX that is used for other things I think you would want to create a repository layer that uses something like auto mapper or manual projections to query your Entities and return your business objects.
If you have a domain model of code based business objects and you have an EDMX that is not used for other things other than persisting your business objects I would say that you need to express your domain in an EDMX and then map it onto your existing database. This is really the use case for an ORM. Having two domain models and mapping from one model to the other where one model matches your domain and one matches your database is adding an extra un-needed layer of plumbing.
The latter approach above is what is called "Model First" in EF parlance. There are several articles written about it although the bulk of them just generate the db from the model. You would not do that step, rather you would map your entities onto your existing database.
The basic steps for this are to "update from the database" not selecting any of the db objects (or entities would be created). Or, you can take your exiting .edmx in the designer (which is sounds like you have) and modify the entities to match your business domain. Or just delete all the entities in your EDMX model, create your entities as you want them, and then map them all.
Here is a jing I made where I use the EF Designer to bring in the model store (the only way to do this is to allow it to generate entities) and then delete the entities allowing the Store information to stay by clicking NO when it asks if you want to delete the table info.
http://screencast.com/t/8eiPg2kcp
I didn't add the POCO generator to this, but if I did it would generate the Entities in the designer as POCO classes.