I am sure that the 0x5xx messages are intended to keep the modules awake. The way that the first bytes of the 0x5xx messages change to match the IDs of the other 0x5xx messages shows that they are working in that way.
Whether they are used in the vehicle for that or not doesn't make any difference to the other messages.
On the log you have three messages in the 0x5xx range, 0x501 from your tester, 0x503 from the HVAC, and, I guess, 0x527 from the DCSM. The 0x5xx messages form a ring, so if you want to keep a ring awake, you need to send the 501#030200 message with a time interval that depends on the total number of 0x5xx messages. I suggested 200 ms when I thought that there was only 0x503 (and the 0x501 message that you were transmitting). Here there are two others, so with the 501#030200 that makes 3 messages, you should transmit at 300 ms intervals to get the ring to work.
What you should get is:-
501#030200
503#271200
527#011200
repeated with one message every 100 ms, so 300 ms for the cycle.
On the other messages, on the CANdump you just posted, I can't see 0x3A0 [8] 45 00 80 02 89 24 00 00 message that you mentioned. All the other messages, starting 0x124, 0x35E, 0x3E7 and 41A#, don't change at all on the CAN log that you posted. It would be interesting to see what those signals do when the controls are operated.
From what I could see on the video, CAN messages that were 8 bytes long were appearing much more often than the group of four, once per second that are in the log. A CAN log and video taken at the same time would allow working out what the messages mean.