As it turns out, information about tests of the Nudol ASAT system has been hiding literally in plain sight - in Jonathan McDowell's log of suborbital launches. A colleague alerted me to the fact that dates and times in the list are quite accurate. "GNIIP" in the table is the GNIIP-53 test site otherwise known as Plesetsk.
The list includes three tests of a 14Ts033 (14Ц033) system, which is apparently the designation of the entire system (rather than 14А042, which appears to be the missile). There were three test launches - on 12 August 2014, 22 April 2015, and 18 November 2015. As we know, only the third one was successful (although none of them involved an intercept).