I can understand the need to target a specialty you know a lot about. But have you given thought to the fact that if you can do Home Health you might be able to do other specialties since that one is a bit harder than others? Just a thought. The return on direct mail is still only 1-2%, word of mouth is great, try resume marketing with a cover letter about your business. Careful with fax blasts if companies are not at least asking for fax inquiries.
I rarely suggest working with marketing companies per se.. the best person to market your service is you. Won't lie.. it takes a while and you will need to get past the cold calling fears. You can't be intimidating and remain confident that you have a service that is in demand. Like I said, it might not be a bad idea to reach OUT to all specialties and market with a specialty in home health care. I did similar and ended up getting referrals from one type of provider who knew another provider that was one of the specialties I billed. When you hire a marketing company or person you usually end up having someone either under or oversell you and that can hurt you present prospects as well as future. Networking with other billing companies might be the way to go so you can get some ideas on some marketing tactics that have worked for others.