Is the aforementioned speech to the wife—despite its lack of seriousness—considered a disparagement of the Qur’an and prayer, and ought it not to have been said?

Your words do not contain mockery of the Qur'an, but there are matters that need attention: First: You should ascertain the nature of the elevator's sound. Is it a melodious, rhythmic, recorded sound or not? Sounds emanating from inanimate objects, if produced by human action and are melodious and rhythmic, are called music. Second: You must be diligent in performing prayers in the mosque with the congregation and arrive early to catch the first takbir. You should not be preoccupied with sounds that may occur in your absence, for the Prophet, peace and blessings be upon him, said: "Whoever hears the call [to prayer] and does not respond, there is no prayer for him except for one with an excuse." Third: You should coordinate with the restaurant's representative to have them deliver at a time other than prayer times, and do not allow your wife to meet with foreign workers in your absence, due to the danger of being alone with non-mahram (definition) women. For the Messenger of Allah, peace and blessings be upon him, said: "Beware of entering upon women," and he said: "No man is alone with a woman but the third of them is Satan."