Use LambdaMetafactory to invoke one-arg method on class instance obtained from other classloader

Based on this stackoverflow answer, I am attempting to instantiate a class using reflection and then invoke a one-argument method on it using LambdaMetafactory::metafactory (I tried using reflection, but it was rather slow).

More concretely, I want to create an instance of com.google.googlejavaformat.java.Formatter, and invoke its formatSource() method with the following signature: String formatSource(String input) throws FormatterException.

I have defined the following functional interface:

@FunctionalInterface
public interface FormatInvoker {
  String invoke(String text) throws FormatterException;
}

and am attempting to execute the following code:

try (URLClassLoader cl = new URLClassLoader(urls.toArray(new URL[urls.size()]))) {
  Thread.currentThread().setContextClassLoader(cl);

  Class<?> formatterClass =
      cl.loadClass("com.google.googlejavaformat.java.Formatter");
  Object formatInstance = formatterClass.getConstructor().newInstance();

  Method method = formatterClass.getMethod("formatSource", String.class);
  MethodHandles.Lookup lookup = MethodHandles.lookup();
  MethodHandle methodHandle = lookup.unreflect(method);
  MethodType type = methodHandle.type();
  MethodType factoryType =
      MethodType.methodType(FormatInvoker.class, type.parameterType(0));
  type = type.dropParameterTypes(0, 1);

  FormatInvoker formatInvoker = (FormatInvoker)
    LambdaMetafactory
        .metafactory(
            lookup,
            "invoke",
            factoryType,
            type,
            methodHandle,
            type)
        .getTarget()
        .invoke(formatInstance);

  String text = (String) formatInvoker.invoke(sourceText);
}

When I run this code, the call to LambdaMetafactory::metafactory fails with the following exception:

    Caused by: java.lang.invoke.LambdaConversionException: Exception finding constructor
        at java.lang.invoke.InnerClassLambdaMetafactory.buildCallSite(InnerClassLambdaMetafactory.java:229)
        at java.lang.invoke.LambdaMetafactory.metafactory(LambdaMetafactory.java:304)
        at com.mycompany.gradle.javaformat.tasks.JavaFormatter.formatSource(JavaFormatter.java:153)
        ... 51 more
    Caused by: java.lang.IllegalAccessException: no such method: com.delphix.gradle.javaformat.tasks.JavaFormatter$$Lambda$20/21898248.get$Lambda(Formatter)FormatInvoker/invokeStatic
        at java.lang.invoke.MemberName.makeAccessException(MemberName.java:867)
        at java.lang.invoke.MemberName$Factory.resolveOrFail(MemberName.java:1003)
        at java.lang.invoke.MethodHandles$Lookup.resolveOrFail(MethodHandles.java:1386)
        at java.lang.invoke.MethodHandles$Lookup.findStatic(MethodHandles.java:780)
        at java.lang.invoke.InnerClassLambdaMetafactory.buildCallSite(InnerClassLambdaMetafactory.java:226)
        ... 53 more
    Caused by: java.lang.LinkageError: bad method type alias: (Formatter)FormatInvoker not visible from class com.delphix.gradle.javaformat.tasks.JavaFormatter$$Lambda$20/21898248
        at java.lang.invoke.MemberName.checkForTypeAlias(MemberName.java:793)
        at java.lang.invoke.MemberName$Factory.resolve(MemberName.java:976)
        at java.lang.invoke.MemberName$Factory.resolveOrFail(MemberName.java:1000)
        ... 56 more

I've read through a number of stackoverflow answers about LambdaMetafactory and read the LambdaMetafactory documentation, but have not been able to figure out what I am doing wrong. I am hoping that somebody else will be able to.

Thank you in advance for your help.