I took a look at a dozen Israeli companies that do business in the West Bank settlements, and between my experience and that of other members of the questioner's group, here is an "answer" to this query.
As the questioner said, the Who Profits? project is the best starting point for researching connections between businesses and the Israeli occupation industry. The data on this site is compiled by The Coalition of Women for Peace, "a leading Israeli feminist peace organization, dedicated to ending the Israeli occupation of the West Bank, Gaza and the Golan Heights and reaching a just peace in Israel/ Palestine" (from whoprofits.org/About.php).
Who Profits will give you names of CEOs, owners, parent companies, and subsidiaries. You can then search-engine them (as well as the names of the companies, of course) to see what comes up on the open Web. I added the terms "new york" and "brooklyn," plus terms related to the business in question, as needed to help channel the results into something relevant. For example, "'eyal peled' 'new york' engineering" (Eyal Peled is one of the owners of Peled-Klein Civil Engineering).
I also tried a number of subscription databases. Thomson Research and Bureau van Dijk Electronic Publishing's Osiris had profiles on the one publicly traded (on the Tel Aviv Stock Exchange) company in the batch I worked on, and that information includes members of the board of directors and some institutional shareholders.
IHS Global Insight and Gale Business & Company Resource Center offered little, though the latter has an entry for the IDB Group (which controls the Irish company that is a partial owner of Nesher Israel Cement Enterprises) that mentions its stated interest, as of 2008, in entering the Las Vegas real estate development market. But even if it were NYC and not Las Vegas, that sounds like a pretty distant path to Nesher. You don't want to attempt to exploit a connection so tenuous that it makes your organization look like it's foolishly grasping at straws.
Finally, I searched some news databases (WilsonWeb Business Full Text and ProQuest ABI/Inform Global) but found nothing at all or at least nothing relevant on the companies.
As a business librarian colleague confirmed, it's really difficult to find information about private companies, particularly if they're overseas (and you're searching only in English-language resources). Unless you happen to stumble on a useful piece of data that's been put in a fixed form, like on a website or in reportage or in a company filing, even wide-ranging searching will not be enough. Here, I think, we come to the line between librarian skills and investigative journalism ("site visits" are among the ways that The Coalition of Women for Peace gets their information for Who Profits, and they don't mean websites).