I've worked at the IRS, so I might be able to offer some perspective. Although government offices in movies may be sleek, futuristic command centers, in reality, most of the IRS is desperately understaffed, running Windows XP on desks that quite literally date back to WWII. Sucking at the government teat isn't as glamorous as it sounds.
The office in question is set up to allow citizens to look up one nonprofit, or ten, or one hundred, for purposes of accountability and investigative journalism. They simply aren't set up to dump seven million tax returns just because reasons. They probably have no reason at all to cooperate with your project, aside from what's required by law.
So by all means tweet away, but I don't think the head of EO pays much attention to Twitter. Shocking that anybody could ignore that fount of wisdom, but hey, bureaucrats, amirite?