I'm sorry.. but the problem stems from the fact that you bought a seperate ticket from HKG to SYD via SIN. Ok, giving you lots of time for connection. You opted for a 5 hour connection. For places like HKG, a 60 min connection is enough. Even on seperate tickets ! So when SQ moved the flight earlier,but you want guarantees from SQ to put you on United ! Of course SQ won't do that - not on a special ticket. You want options, then you get a fully endorsable, refundable, reroutable ticket.

LH in my opinion has always been on time. But yes, Murphy's Law comes into play when its your flight. SO you do what normal people would do. Book your LH flight to leave a day earlier, and spend a day in HKG at your own expense.

Or else cancel your LH ticket and buy an entirely new ticket that combines the a SQ flight to SYD. So if your LH flight is delayed, then LH would take the necessary steps to ensure you get on your connecting flight. SQ too, would also ensure you get onto SYD from SIN on the SQ ticket. You said that LH has been accomodating, due to an illness in the family. Then take this matter at hand and let them reissue your ticket to a new one then.

SQ has done all they can to accomdate you. But it is you that is being unreasonable in your asking for guarantees and compensation. You want to change your flight, sure SQ will just put you on waitlist if the flight is full. You want to move it a day later, ok that's fine too. But as it is an originating ticket from HKG, it is not their problem if you voluntarily moved your flight. So there would be no compensation... or hotel.

Sorry to sound harsh. But if you want guarantees, then buy a through ticket all the way to Sydney. Then if you're delayed enroute, then you will be assisted.