Today I saw the following in a contract on EDGAR (emphasis added):
Owner shall provide Contractor notice (which may be oral or by electronic means) of such non-compliance and Contractor shall correct such non-compliance right away …
So add right away to the list of alternative ways of saying promptly. MSCD 13.536 already offers expeditiously, as soon as practicable, and forthwith.
Elegant variation—going out of your way to avoid using the same word or phrase twice—is never a good idea. It’s particularly unfortunate in contract drafting, in which tone plays no part. If you wish to convey the same meaning, use the same word. If you think you’re exploiting shades of meaning by using, say, right away instead of promptly, you’re fooling yourself, as no such distinctions exist among vague words and phrases of that sort.
(Bonus: Regarding the relationship between promptly and immediately, see MSCD and this 2008 post. And of course, see this recent post on not saying the negative equivalent of promptly.)