Since you are internal i would suggest connecting with all the med schools in Texas, start recruting while they are still finishing residency or fellowship. Many of the new docs start looking six months before they finish residency or fellowship and have signed contracts before they finish. The different specialty boards have web sites that have career pages where you can start to build a pipeline and sometimes find experienced docs that are ready to make a move. It's a long cycle as many have to complete a contract or your hospital has to be willing to buy out their contract for them to be released.
There are a lot of docs on linkedin with more and more becoming active on twitter. #hcmc is the healthcare med chat, check out who all of them follow. They are touchy about recruiters interjecting into their dedicated medical chats but you can pick up some good connections for different specialties particularly those who are department heads at teaching hospitals who supervise residents. They are normally helpful.
You represent a prestigious organization so marketing openings should get you some good docs who are interested in a hospital practice.
Sandra - offered a lot of great tips there. I would also suggest not going with the shotgun approach. You will have much more success if you are able to focus in on one or two specific specialties. This way you really will be able to make sense of all the information you are taking in and share back in such a way that you appear an expert in the marketplace. For the first 5 years of building my desk I only recruited OB/GYNs. By talking to so many of them you learn about malpractice, call, and surgical procedures. Once you fully understand what is important to them in a job, you will find much more success in being able to sell the open reqs you have. I would be more than happy to help with any specific questions as you get going. Feel free to reach out at anytime.