Restricting list extensions

Hello Groovy users/devs

I have a derived class from List (lets call this MyImmutableList) and I
want to only allow the use of certain extension functions. For example,
collect is ok, but left shift is not

myImmutableList << 100 // I want to prevent this because its an immutable
list)
myImmutableList.collect { it + 1 } // This is ok

How do I achieve this? I have my own AST transformations and I can detect
the use of the MyImmutableList class. My first guess is

   - Enable Static compile
   - Post static compile, detect all extension methods and the object
   inferred_type it is called on. If type is MyImmutableList, check if
   extension method is allow listed. If not cause compile error

I am not sure if this is fool proof. Are there easier ways to do this? Is
it possible to get the static compile mechanism to tie unknown methods to a
default method that I can check for and just error on?

regards
Saravanan