You have two distinct but related challenges: learning about "reliable distributed systems" (eventually you will discover that is an incomplete specification within a large and complex field); and getting a job in that field at some point in your education.
Two activities are crucial to the education challenge: becoming familiar with the pertinent literature; and experimental implementations. I infer that your interest is at the infrastructure (e.g., middleware) level rather than at the application level. There are fewer infrastructure experts than application experts, just as for operating systems. OS and middleware experts need the expertise to make programming easier for their users.
I am going to assume that you want (as you should) to begin to understand the principles of distributed systems, not just programming techniques. Most of the foundational literature is in a relatively small number of research journals and conference proceedings, and in a relatively small number of books (textbooks and research monographs).
The research literature is essential but oriented toward subject matter experts, so you should start with some textbooks. Unfortunately, IMHO currently there are no really good distributed (especially reliable distributed) textbooks. Some are too narrow and deep, some are too out of date, some are too shallow. When I taught a distributed systems course at CMU, I created balanced contemporary lectures augmented by synthesizing a "book" from a number of journal and conference papers, and I would do so again today. But given the need to purchase a book (or two), with considerable reluctance I recommend Ghosh "Distributed Systems: An Algorithmic Approach," plus Coulouris et al. "Distributed Systems: Concepts and Design (5th Edition)."
For the next level of detail, I suggest focusing on publications in the ACM and IEEE Computer Society Digital Libraries. You can search them using Google Scholar or at their web sites. Depending on your motivation and finances, you might consider paying for PDF downloads from these libraries. I particularly recommend that you explore the Proceedings of the ACM Symposium on the Principles of Distributed Computing, and the Proceedings of the IEEE International Conference in Distributed Computing Systems. Amazon has a vast collection of in-depth books on almost every aspect of reliable distributed systems.
Soon after you begin your study of the principles in the literature, you should do some experimental design and implementation.
The most accessible way is to use an open source version of Linux running on at least three PC's connected by an Ethernet. For your purpose, the PC's can be very inexpensive out of date units. It is important that you find a community of interest around the Linux version so you are not on your own. That community should be academically based, not associated with some Linux product, to give you freedom and support to experiment with your own version.
I have not looked around recently for candidates, as you should. But I know one very well: Virginia Tech's ChronOS, http://www.real-time.ece.vt.edu/chronos.html. ChronOS has a feature important to your interest in reliable distributed systems: it includes an unusual emphasis on some state of the art distributed fault management concepts and techniques. It also emphasizes real-time, which may be peripheral to your interests, except that performing distributed fault management in real-time is exceptionally challenging, and would provide you some rare subject matter expertise that conceivably could help in your search for employment. ChronOS is led by Prof. Binoy Ravindran, http://www.real-time.ece.vt.edu/ravindran.html, firstname.lastname@example.org. Although the ChronOS community of interest is not as large as that of some other Linux versions, it is likely to be flexible and supportive of your desire to study it and make changes to your own version. It may be possible that you create features that Binoy wants to include in the baseline ChronOS.
As for your second major challenge, to get a job in the field of reliable distributed systems, there are the obvious generic ways to search for opportunities. But if you are a budding subject matter expert on reliable distributed system infrastructures, though that is a niche, it is a very important one (e.g., more people program microprocessors than design them, but microprocessor designers are obviously essential). There are vendors of middleware and so-called enterprise system buses, such as Oracle, TIBCO, etc. (you can locate them easily). Note that there are application domains that at least sometimes if not frequently create their own application-specific middleware or modify commercial products: defense (extensively), telecommunications, and industrial automation.