Trying to decode LEV-1

LEV-1 is a small lunar hopper that was carried by the SLIM lunar lander. It was released a few metres above the surface on January 19, as part of the lunar landing of SLIM. LEV-1 transmits telemetry in the 435 MHz amateur satellite band (it has an IARU satellite coordination approval), and also in S-band. Shortly after the landing, CAMRAS received the 437.410 MHz signal from LEV-1 using the 25 m radiotelescope at Dwingeloo. They have published a couple of IQ recordings in their directory of miscellaneous recordings (see the filenames starting by slim_).

The information about the telemetry signal of LEV-1 is scarce. Its website just says

Telemetry format of LEV-1 stands on CCSDS. The contents of telemetry are under developing.

The IARU coordination sheet contains other clues, such as the mention of PCM/PSK/PM, CW, and bitrates of 31, 31.25 and 32 bps, but not much else. Regardless of the mention of CCSDS, I have found that the signal from LEV-1 is quite peculiar. This post is an account of my attempt to decode the data.