Listen

If you Listen to the customer they will always give you the path to a successful move.

Yes- the customer is ultimately always right and you will never win in the end if you oppose them or try to give them all your years of wisdom in the moving business in five minutes.

I understand that you are the boss and the crew chief and you know what needs to be done BUT remember who is paying.
Listen.

Also when you first walk the house with the customer ask questions of course but more important this is where they will really tell you what is of most importance to THEM.
It may not necessarily be the most expensive items in the house either, it may some piece that has a lot of sentimental memories to it for them.
Listen.

In any case when they seem concerned you need to express YOUR concern. Yes, you may know that you have it under control and it may not be a big deal to you but you need to remember that this is THEIR move and they need to know that you care about what concerns them.
Listen.

Find out what is most important to them and mother it , and try to do it in front of them .
Show them you care.