I am afraid this is still happening. I am cleared to a certain flight level, then no more instructions to ascend (the whole flight, if I leave it). After a time I check in with ATC, and the pilot voice says (in this case) 'Out of Flight Level 210 for Flight Level 350'. ATC: 'Roger...'. No such instruction to climb has been given however (verified by onscreen ATC Communication Log).
I took a more careful look at your log for the YSCB-YMHB flight. The log shows you were handed to Control at 20:07:54 (and the frequency was changed at that time):
20/05/2018 20:07:54: 950 - Transcript: 'Quantas 7385 Contact CONTROL on 129.5 '
but according to the log your first check-in with Control was at 20:16:06:
20/05/2018 20:16:06: 760 - Transcript: 'CONTROL Quantas 7385 with you out of Flight Level 210 for Flight Level 350 '
The log shows no use of hotkey 0 or check-in between those times. At 20:12:21 Control told you to resume own navigation (you were tuned to the correct frequency) and you responded, but there was still no check-in until 20:16:06. The lack of a check-in before you reached your first clearance altitude may be the reason for the missing climb instructions. Maybe for some reason your check-in hotkey wasn't detected. Be sure to check in and get a response from ATC. (This would also explain why there are no problems when using Mode 2.)