This is a craft-your-own career situation.
1. To address EA vs CPA - An EA has the credentials and background to do what you want, BUT to have true control over your career, the CPA has more prestige. If you start your own firm, the individuals that you want to serve are far more familiar with a CPA. They don't know what an EA is and you'll have a harder time impressing them with your certificate. Individual clients are usually impressed by fancy certificates. Therefore, CPA is better for you. Having an EA instead of a CPA also limits your ability to get promotions if you decide to stay in a traditional public accounting environment. There is no reason to have both.
2. It sounds like you're still in school. The main thing you'll need to do when you graduate is seek out jobs at smaller firms. There will be a lot of pressure to go with Big 4 accounting firms but they won't get you the experience that you need with individuals/families and non-commercial rentals. For that you want a local firm, or a small national/regional firm. Keep in mind that salary at these types of firms may be a bit less than more prestigious Big 4 jobs - which leads me to my next point.
3. I suggest starting your own practice after a couple of years of experience. You'll suffer from wage stagnation at smaller firms if you stay there long (and yes, they will make you work on clients you don't care about). In order to truly shape your individual/rental focused career, you'll need to take control of it and focus on acquiring the kinds of clients you want, while avoiding those that you don't like. From there, you'll want to go around telling people that you're a rental property expert. Try to make it as true as possible by doing continuing ed and reading up on rental taxation (you'll also want to become very familiar with self-directed IRAs, which are a great tool for rentals).
So to answer your question - yes - this job exists. The ultimate job title is probably Self Employed CPA. The stepping stone job title is just tax associate.
The key to success here is that you need to take control of your own career. Don't quibble - if someone asks what you're interested in, tell them you want to be an individual tax/rental expert. Ask interviewers if they can give you that experience at their firm. Tell your managers that these are the types of clients you want to work on.
It would take time to build a practice that is only individuals and rentals. Individuals tend to own companies and start businesses, and you probably won't kick them out when they come to you with that. But you can certainly market yourself as a rental expert and cater to that kind of clientele.
Keep in mind that while older, established firms may be bound by the local market - you don't have to be. If you go out on your own, there's no reason your clients have to be local. The right website and software tools will allow you to attract remote clients from all over the country, which can be an asset when you want to be a niche specialist.
