We know the calls were made in succession, as they were described by Stoddard at the hearing as the 1st, 2nd, and 3rd call (with person/place called also described). Spice had the info that the last call ended at 4:32 - and presumably that was also the call he was actually talking to someone on (the other two calls didn't get through, according to testimony). So if that call ended at 4:32, and that was the call in which LE overheard him say to someone that his child had died, it's apparent that the altercation must have come right on the heels of that last call--because LE were also telling him to "get off the phone." (There were no calls on record after that 3rd call, the one to daycare.) He then was handcuffed and put in the patrol car, and I doubt was calling anyone after that. So...maybe spice can link us to something that shows that 3rd call, the 6-min. one, ended at 4:32?
Maybe it's over in the timeline thread...I'll go check.
ETA: I believe I read that the firetrucks and ME truck were the last to arrive on the scene, so I'm guessing they were probably securing the scene, taking photographs, talking to witnesses, and/or awaiting the ME at the time LH was trying to call RH.
ETA: Cooper's body was still on the scene at 5:45 PM, so ME truck didn't pull away until after that