I don't think you need an LLM. I think a JD would help you more with your career. I know a couple CPA's who got JDs and now do a combination of estate planning and tax. Both of them had opportunities to do LLM's but their prospective employers recommended against it.
If you have a passion or a desire to practice tax law, bankruptcy, family law, or criminal law, you can do so as long as you OK in school. (By contrast, it takes a ton of talent, skill, and luck to be an entertainment lawyer or a BigLaw M&A guy).
I don't usually tell anyone to give law school a second look (Statistically it's not a great decision for a large minority of students). In your case, I think you should really think about doing a J.D. if you can get into a school in the area you want to work. Tax and Estate law are more predictable, your clients are likely to pay, and most of your clients will be happy. If you stay on the transactional side, you'll have less emergencies than most other practice areas. However, if you work on estate litigation (will/trust contests and probate) you'll get emails from the occasional pissed of client at night or on the weekend.
Beware of law school, unless you are a science rock star and want to do IP, or unless you are a Tax rock star and want to do Tax/Estate.
My four cents.