Cheylev; who said there’s even a chiyuv m’dina to say tachanun?
Also, reb e, there’s a better reason to justify davening late. Rav Meir Shapiro said that a rebbe is toraso umnaso, and is hence patur from davening in general; he can daven a tefilas nedava whenever he wants.
Rav belsky said this over once on a shabbos; i asked him, how would this work for the chasidim, who are not toraso umnaso? He said with a smile that they’re farbunden with the Rebbe. He was litvish, but had a deep respect for chasidishe minhagim, with some exceptions.