My thoughts, for what they're worth:
To absorb style, it's my opinion that you should read a lot of material written in the style you want to absorb. Basically, you gain familiarity through exposure. (This will do nothing for your accent. Accent, as you say, is hard to change without a lot of conscious effort.) I'm not sure where you'd find this material, though. Maybe class materials from a well-regarded business school?
The advice is common to develop skill in a target language by picking up a girlfriend who speaks it natively. For your purposes, this is dangerous; you'd need to be sure that your partner was the correct social class (not that difficult, if they already hold the type of job you want), and that you don't pick up a style of speaking that tends to suggest to natives that you are the opposite sex (this is a big risk).
Speaking with a noticeable foreign accent will mean a lot of people don't find it odd that you make grammatical mistakes. Your mistakes are quite minor; as long as your accent isn't preventing people from understanding you, you might well be better off keeping it.
Finally, based on your comment I wouldn't expect you to have any trouble conveying or receiving information in English. Furthering your English is basically a vanity project. (Not to say that it wouldn't be helpful in career advancement -- it might be! But you're well past the point where misunderstandings are a risk.)
I hope some part of this was helpful.