Advantages of taking the Subject GRE exam in April
Your approximate dates for start of term and for graduate application availability are correct.  Some are open through January and some even as late as February, although most PhD applications do close in December AFAIK.

If you're not finishing until 2018 then the only real advantage is that taking the GRE in April will allow you to take it again in September if you need to improve your score.

Of course you could also take the October one if it's offered in your area, but you won't get September's scores back until after the October registration deadline.  And the October test's approximate score reporting date of December 9 may be too late for some applications.  IIRC, some applications close on or very close to December 1, but TBH it's been a long time and maybe that's not right.

On the plus side, there's a new rule in place ("new" relative to 2006ish) where you can submit only the score(s) you want to the schools.  In the past you had to submit everything on your score report, good or bad.

Sources:


https://www.ets.org/gre/subject/register/centers_dates
https://www.ets.org/gre/subject/scores/send/asr


My recommendations:


If you really feel like you're fully prepared for the April test, then take the April test.  If you don't do as well as you wanted then you'll have time before the September test, and you'll have time to earn extra money to help pay for it.  Tutoring is always an option, and if you tutor subjects that are on the GRE then that's a double bonus.
If you aren't confident you can be fully prepared for the April test, don't take the April test.