Hey Andrew
The problem you have is using Model.Items as a parameter. The code
<%= Html.DropDownList("items", new MultiSelectList(Model.AvailableItems,
"id", "name", Model.items), new { multiple = "multiple" })%>
isn't actually working as you would expect. It's working because the name of the dropdown is "items". That's because there was a form param called "items" posted back to your action. That param gets stored in the action's ViewState (don't confise with ViewData).
The Html.DropdownList() sees that there is a ViewState param named the same as you have named your dropdown and uses that ViewState param to work out the selected values. It completely ignores the Model.items that you passed in.
If anyone can explain the logic of not being able to override the default behaviour then I'd love to hear it.
So, that's your first problem. To get around it all you have to do is to rename the dropdown to something else - exactly like you did in your second example. Now your second problem comes into play: the list of selected items must be a collection of simple objects (I think it actually needs to be an IEnumerable but I'm not 100% sure).
The DropdownList() method will try and match those selected values to the Value in your AvailableItems collection. If it can't do that it will try to match against the Text.
So, try this to see if it works
<%= Html.DropDownList("somethingelse", new MultiSelectList(Model.AvailableItems,
"id", "name", Model.items.Select(c=> c.name)), new { multiple = "multiple" })%>
Good luck