Hi Tom... with you on the SO tone ... here's what I think is going on:

1. An empty Array is falsey, yet an empty shaped Array is truthy (I would be interested to know why!) - thus, as you have already noted, the original error message is wrong in the suggestion for TWEAK. (You may wish to raise a bug issue at rakudostar on git.) More at https://stackoverflow.com/questions/67373726
2. You are getting a compiler warning from trying to say ~$hamper.items where there is an empty value (Any) in a shaped Array... this does not happen with a non-shaped Array as the length auto-adjusts to the contents.

   Use of uninitialized value element[2] of type Any in string context.
   Methods .^name, .raku, .gist, or .say can be used to stringify it to s
   +omething meaningful.
     in block <unit> at test.raku line 14
   [download]

   So, I propose you implement a Str method to bypass (Any) elements and format the object output for .put (or say ~$hamper).
3. Array elements are each scalar containers and are each rw in any case - has @.items is rw just allows the top level array to be assigned to via a generated setter method. (NB. TWEAK can use the private @!items variable directly to assign the defaults).
4. You can see this now gives low boilerplate accessors that do what you want (?) and protect from writing beyond 3 elements.

class Hamper {
    has $.name = 'Christmas Basket';
    has @.items[3];

    method TWEAK {
        @!items = ['Mince Pie', 'White Wine', 'Stinky Cheese'] unless 
+@!items.any.so;
    }   
    method Str {
        "Name:  {$!name}\nItems: [{@!items.grep(*.so).join(', ')}]\n";
    }   
}

given Hamper.new {
    .items[2] = 'Hard Cheese';
    .put;
}
#Name:  Christmas Basket
#Items: [Mince Pie, White Wine, Hard Cheese]

given Hamper.new( items => ['Fish', 'Canoe'] ) { 
    .put;
    .items[2] = 'Bicycle';
    .put;
    #.items[3] = 'Horse';     #fails.. Index 3 for dimension 1 out of 
+range (must be 0..2)
    #.items.push: 'Blue Nun'; #fails.. Cannot push a fixed-dimension a
+rray
}
#Name:  Christmas Basket
#Items: [Fish, Canoe]

#Name:  Christmas Basket
#Items: [Fish, Canoe, Bicycle]
[download]