I think your misgivings are well placed actually. In a factory environment, you can control the reed plate fixture and it can be solid, offering no sympathetic vibrations.
Once mounted in the melodica, tuning readings, particularly when checked by vibration, include the vibrations of the melodica body. That is why, I believe, some of the notes I pinged did not produce any reading until I changed the tuner position. Many other notes produced readings that were too uniform to believe. It would take a development effort to perfect this technique.
I am not going to develop it. I had forgotten people may have explored this possibility.
I just imagined having a post inside the reed chamber where you could attach a tuner and tune the whole melodica with the cover off! What a time saver.