When you are looking for movers, you need to split the marketplace between the full-service movers who pack, transport and unpack for you and the the guys with a truck variety who will pack only large bulky items for you and will deliver and unpack only what they packed.
The difference in pricing between these two groups is huge! Can vary from +$2000 for a full service move to $450 for a single load on a 10ft truck.
In the full service category:
Crown Line: My friend - a snr manager for major MNC's local delivery/logistics company serving retailers - told me that Crown Lines is generally recognized as the best within SG. I tried to call them, but they were completely unavailable for the dates I wanted.
SIR Moving Services: They are NOT cheap. I'm about to use them as they seemed the most professional and responsive of the movers I asked for quotes. I will update with my experience.
Moving Insurance:
The standard is to charge 1.5% of the assessed value of your belongings. That is VERY high. I was told that this is because there are only two underwriters issuing these policies. The better option is to get a renter's or homeowner's insurance that covers your belongings during moves domestically. Only one I know for now is HSBC. Their policies are underwritten by AXA, but AXA's own policies don't offer this, nor does AIA, AIG, or Great Eastern.
* I don't have any commercial affiliation with any of the services I mention, nor does anyone I mention as a reference for the services.