How does def keyword work in Groovy?

this one helps. As you say, it's not going to be easy to change the asType method for Integer to accept X as a new type of transformation (especially without destroying the existing functionality).
The best I can think of is to do:

Integer.metaClass.toX = { -> new X( delegate ) }

3.toX()

// Get a handle on the old `asType` method for Integer
def oldAsType = Integer.metaClass.getMetaMethod( "asType", [Class] as Class[] )

// Then write our own
Integer.metaClass.asType = { Class c ->
  if( c == X ) {
    new X( delegate )
  }
  else {
    // if it's not an X, call the original
    oldAsType.invoke( delegate, c )
  }
}

3 as X

will be helpful for those in need Moving this from comments. To make IDEA see the jars used by Groovy Grape, put your caret on the @Grab annotation in your code, press Alt+Enter and choose "Grab dependencies".

I hope this helps . if you compile it as a Script, groovyc will just ignore the final keyword, but if you wrap it into a class, groovyc will raise a compilation error.
fin.groovy with content

final String x = "a"
x = "b"

$ groovyc fin.groovy

import org.codehaus.groovy.reflection.*;
import java.lang.ref.*;
import groovy.lang.*;
import org.codehaus.groovy.runtime.*;
import org.codehaus.groovy.runtime.callsite.*;

public class fin extends Script
{
    private static /* synthetic */ SoftReference $callSiteArray;

    public fin() {
        $getCallSiteArray();
    }

    public fin(final Binding context) {
        $getCallSiteArray();
        super(context);
    }

    public static void main(final String... args) {
        $getCallSiteArray()[0].call((Object)InvokerHelper.class, (Object)fin.class, (Object)args);
    }

    public Object run() {
        $getCallSiteArray();
        String x = "a";
        return x = "b";
    }

    private static /* synthetic */ CallSiteArray $createCallSiteArray() {
        final String[] array = { null };
        $createCallSiteArray_1(array);
        return new CallSiteArray((Class)fin.class, array);
    }

    private static /* synthetic */ CallSite[] $getCallSiteArray() {
        CallSiteArray $createCallSiteArray;
        if (fin.$callSiteArray == null || ($createCallSiteArray = fin.$callSiteArray.get()) == null) {
            $createCallSiteArray = $createCallSiteArray();
            fin.$callSiteArray = new SoftReference($createCallSiteArray);
        }
        return $createCallSiteArray.array;
    }
}

class A{
    final String x = "a"
    def a(){
        x = "b"
    }
}

$ groovyc fin.groovy 
org.codehaus.groovy.control.MultipleCompilationErrorsException: startup failed:
fin.groovy: 4: cannot modify final field 'x' outside of constructor.
 @ line 4, column 3.
   x = "b"
   ^

1 error

it fixes the issue import class into another Keyword class and declare its object to use that Keyword.
Root Navigation Keywords

public class RootNavigations {

    final dialog = new Dialog() // ******* imp step

    @Keyword
    def checkDialogWorking() {
      WebUI.click(findTestObject('App/Page_Home/btn_OpenComparisons_Dialog_Home'))
      this.dialog.clickCancel() // ******* imp step
    }

    ...
}