I'm assuming you already have all of your referring physicians on board for their part of the cost as well?
The third party will just be a broker for you.
You could create direct links between your EHR and each one of your referring physicians and use HL7 to send to them.
We have HL7 with several EHRs and labs, etc.
We also have a HL7 with a central hub, in my case called NeHii. My patients are linked to me (not sure how, I didn't do it) and inform that comes into the hub matching at least 2 identifiers is automatically pulled by my system into my DB and sorted as desired.