I am going to give you some hard facts as someone who is a New York qualified lawyer. If you want a shot at very good law school for an LLM, you also need either really great marks or really stellar experience. Your work experience may be good for that (though I don't have the details). For financial aid/scholarships, especially the merit based ones, you need both good grades and good work experience. Good news is, your past institute doesn't matter. But you need recommendations from your past professors. Keep that in mind.
Jobs post LLM are quite competitive and I'm not going to lie - law firms there are very picky about which LLMs they hire. People with past experiences from more transactional practices in big law firms in India tend to get a preference. Networking will be key in the LLM.
However, for the JD, your legal experience and admission to the bar in India may give you an edge in admission. But you need to get a kickass score in LSAT to get a good school and unfortunately your undergrad grades may be considered. But, JDs are expensive. You'll have to take out a loan if you don't get good financial aid.
These are the routes available to you. As for the New York Bar, you need to get your undergrad school to send your transcripts to them for vetting. There is no getting around it.
Anyway that's my two cents for the law.
If you're not too opposed to it, go for an MBA.