If I were a betting girl, I'd wager that he got rid of the crime-worn jacket the minute the video of him wearing it became public.
He kept the gun precisely because he had no clue that the same video showing him wearing the jacket also picked him up cycling the round into the chamber. Nor did he have a clue that he had inadvertantly left a bullet between their bodies. Those bits of information were witheld from public consumption.
By the time RA found out they had evidence he had used the gun to subdue (cycling) and, worse yet, had actually left a round at the scene ... they were snagging the search warrant and it was too late for him to do a darn thing about it.
Good on LE.