As it turns out, there is more information about the Project 4202 test record than I knew existed. A Twitter post drew my attention to a very detailed table of Soviet/Russian launches that Jonathan McDowell keeps on his site. The table has an unusual amount of detail in that it includes serial numbers of launchers. (Jonathan also maintains a master list of all launches, which includes those for which serial numbers may not be available.)

In the list, the Project 4202-related launches are designated 15A35P, after a modification of the 15A35 UR-100NUTTH/SS-19 missile. There are nine tests of this type in the table and in general the details correspond to the information collected from other sources (note that I corrected a couple of dates in that table). There are important additions as well, but there are interesting differences and omissions. Below is a combined table that shows all known and suspected tests related to the program.

15A35P Other date Comment
28 Feb 1990 28 Feb 1990
29 Mar 1990 5 Mar 1990 The same test. March 5 appears to be a mistake
26 Nov 1991    
28 Jul 1992    
27 Jun 2001 27 Jun 2001  
18 Feb 2004 18 Feb 2004  
27 Dec 2011 27 Dec 2011
  27 Sep 2013 Considered confirmed
  Sep 2014? Not confirmed
26 Feb 2015 26 Feb 2015  
19 Apr 2016 19 Apr 2016  

First, there is a puzzle of the second test in 1990. I assume that the date March 5, 1990 is incorrect. The "serial numbers" table is very detailed, so it is highly unlikely that it got the date wrong. March 5th also comes from a fairly reliable source - one of the documents in the Katayev archive. The document says two test had taken place - on February 28 and March 5 [sic]. I think it is entirely possible that the date got corrupted somewhere in the process and the correct date is indeed March 29. Besides, I always suspected that there is something wrong with having two tests that close together - less than a week. So, March 29, 1990 it is.

The August 1990 meeting also discussed an upcoming test, this time "with separation" [of the vehicle from booster]. Everything was supposed to be ready by October 1990, but it appears that the launch was postponed and that third test took place in November 1991. The Soviet Union broke down shortly after that, but the program apparently had enough inertia in it to carry out a fourth test in July 1992. Then the program froze for almost ten years.

The launches were resumed in 2001 and it appears that the next three tests are identified correctly. Then, the "serial numbers" table has nothing in September 2013, while I am fairly certain that the test did take place. (UPDATE: It is also on Jonathan McDowell's complete list, on September 27) The 2014 test has a much bigger question mark next to it. The evidence is rather circumstantial, so unless there is a reliable confirmation of the launch, it should probably remain there as unconfirmed.