I had the same issue where a private value was not set because Mockito does not call super constructors. Here is how I augment mocking with reflection.
First, I created a TestUtils class that contains many helpful utils including these reflection methods. Reflection access is a bit wonky to implement each time. I created these methods to test code on projects that, for one reason or another, had no mocking package and I was not invited to include it.
public class TestUtils {
    // get a static class value
    public static Object reflectValue(Class<?> classToReflect, String fieldNameValueToFetch) {
        try {
            Field reflectField  = reflectField(classToReflect, fieldNameValueToFetch);
            reflectField.setAccessible(true);
            Object reflectValue = reflectField.get(classToReflect);
            return reflectValue;
        } catch (Exception e) {
            fail("Failed to reflect "+fieldNameValueToFetch);
        }
        return null;
    }
    // get an instance value
    public static Object reflectValue(Object objToReflect, String fieldNameValueToFetch) {
        try {
            Field reflectField  = reflectField(objToReflect.getClass(), fieldNameValueToFetch);
            Object reflectValue = reflectField.get(objToReflect);
            return reflectValue;
        } catch (Exception e) {
            fail("Failed to reflect "+fieldNameValueToFetch);
        }
        return null;
    }
    // find a field in the class tree
    public static Field reflectField(Class<?> classToReflect, String fieldNameValueToFetch) {
        try {
            Field reflectField = null;
            Class<?> classForReflect = classToReflect;
            do {
                try {
                    reflectField = classForReflect.getDeclaredField(fieldNameValueToFetch);
                } catch (NoSuchFieldException e) {
                    classForReflect = classForReflect.getSuperclass();
                }
            } while (reflectField==null || classForReflect==null);
            reflectField.setAccessible(true);
            return reflectField;
        } catch (Exception e) {
            fail("Failed to reflect "+fieldNameValueToFetch +" from "+ classToReflect);
        }
        return null;
    }
    // set a value with no setter
    public static void refectSetValue(Object objToReflect, String fieldNameToSet, Object valueToSet) {
        try {
            Field reflectField  = reflectField(objToReflect.getClass(), fieldNameToSet);
            reflectField.set(objToReflect, valueToSet);
        } catch (Exception e) {
            fail("Failed to reflectively set "+ fieldNameToSet +"="+ valueToSet);
        }
    }
}
Then I can test the class with a private variable like this. This is useful for mocking deep in class trees that you have no control as well.
@Test
public void testWithRectiveMock() throws Exception {
    // mock the base class using Mockito
    ClassToMock mock = Mockito.mock(ClassToMock.class);
    TestUtils.refectSetValue(mock, "privateVariable", "newValue");
    // and this does not prevent normal mocking
    Mockito.when(mock.somthingElse()).thenReturn("anotherThing");
    // ... then do your asserts
}
I modified my code from my actual project here, in page. There could be a compile issue or two. I think you get the general idea. Feel free to grab the code and use it if you find it useful.