My understanding is different from yours: from what I can tell,...

My understanding is different from yours: from what I can tell, it is in HML's court to take actions to get the suspension lifted, not ASX's court.

I understand that while the suspension in June 2017 was initially voluntary on HML's part, it is now involuntary because (as per HML's announcement of 13 March 2018) ASX considers HML to be in breach of Listing Rule 10.1. HML indicated in that announcement that they would seek [retrospective] approval from shareholders for the acquisition of certain securities in John Bridgeman Limited by HML.

I don't understand why HML has been approaching ASX in recent times seeking to have the suspension lifted when no visible progress has been made towards rectification of this breach, but hopefully progress can be made soon!