I think it would be like a musician studying acoustics, or avid dog owner/trainer studying canine anatomy. It probably all depends on what your future goals are with Japanese. If you're planning to move to Japan, or just keeping that option open, and working and perhaps marrying a Japanese, then you should just remain as a JSL (Japanese as a Second Language) learner. Linguistic analysis of Japanese won't be of much pragmatic value, it's too technical, and it doesn't make for good dinner-party conversation. Most Japanese natives aren't even aware of the things that Japanese linguists study, much less care when you tell them about it. If, however, you've lost interest in Japanese as a social hobby, then going the linguistic route is certainly one way to progress in the study of Japanese. But linguistics is a science in the same way that biology or programming is a science in that it is grounded in formal model building. It's going to take a lot of time, and unless you're in school, you won't meet many people that share your interest. It's also not going to help you pronounce or write better. Just like studying calculus won't make you better with mental arithmetic.
They say that linguistics is the most human of the sciences and the most scientific of the humanities, but without a doubt the demand for rigour and the application of the scientific method in linguistics make it a serious science. You should pick up An Introduction to Japanese Linguistics (Tsujimura, 2006). This book contains a short intro to some linguistic theory and applies it to Japanese. Although not a very rigorous book, if you find it boring, then chances are Japanese linguistics is not for you.
I'll show you some of my reading list for Japanese and linguistics books to give you an idea of what others like you might be doing. These are just some of the phonetics and phonology textbooks that I am currently occupied with and would definitely recommend. I haven't yet got to syntax or semantics, nor the other fields of linguistics, so I couldn't tell you what's good to read. Like you, I've been a JSL learner for about 5 years, but studying linguistics for about 1.5 years now. It's just a armchair hobby of mine, but studying linguistics sure has been an expensive hobby due to the cost of textbooks:
- Contemporary Linguistic Analysis, Sixth Edition In my opinion, the only intro level ling text you will need. Very good text. I haven't read later editions.
- Introductory Phonology Really good book once you have been introduced to a little phonology already
- Introduction to Japanese linguistics A little too easy for my taste, but an excellent place to start.
- The Sounds of Japanese with Audio CD Goes into the finer detail of articulatory Japanese, and covers IPA transcription for Japanese. The CD is useless though.
- The Phonology of Japanese A little more advanced, but one of the few textbooks on the subject.
- Acoustic Phonetics You will need to be familiar with Fourier analysis and a little bit of physics and computer science for this one.
- Principles of Phonetics 700 page monster on phonetics. Covers everything up to the acoustic signal analysis aspects of phonetics. I've only read parts of this at my uni library, but it seems like the most comprehensive treatment of phonetics in existence (within a certain level of detail and application of course)
- Mathematical Methods in Linguistics A real eye-opener on just how deep linguistic science is. Covers the mathematical model of language laid down (or at least advanced) by Chomsky. It has some pretty advanced mathematics, some of which certain schools reserve for graduate level classes, but it doesn't presume a background in calculus or linear algebra, so it is accessible, if dense, to a student in any program. Most people are not even aware that this subject matter exists, but if you take your shit seriously, I think you should read this.
- Foundations of Statistical Natural Language Processing Good for starting your own projects in Japanese linguistics. Assumes familiarity with statistical science