I just wrote you a long response in another thread! So you have written references already? They are like gold to most agencies. If Medical Solutions doesn't like them, forget them. Can you imagine redoing your references every time you work with a new agency? There are around 400 agencies out there. Kind of like dating. If something bad happens on the first date, you drop them right away. If you have an established relationship, well that is more valuable so there is more give and take. Something bad happened, forget about them and move on to the next one.
You could give them your references and perhaps they can contact them and duplicate it on their form, but I have written references in no small part because I don't want them called by every John, Dick, and Harry agency.
I have an ER friend with a different tack on getting references. He get them from the physicians! Typed up on their own letterhead no less. Works very well for him, but you have to be in a position to work closely with physicians, and also be the kind of person they are willing to do that for. I've never considered that before, but I recently met an OR tech who also did that (found out from a surgeon much later). Can you imagine having some agency you've never worked with before (so you don't even know if they are any good or not) go to a physician and ask them to type something up on the agency letterhead?