Would the questioner be sinful if he refrained from giving Zakat al-Fitr in cash — as his father insists — and instead gave it on his own behalf as food, knowing the Sunnah, and considering that he lives with his family and is unmarried?

Some jurists have permitted giving the value (money) for Zakat al-Fitr if there is a prevailing benefit in doing so. Perhaps you gave your Zakat al-Fitr as food for yourself, seeking the more cautious approach. If you are able to earn a living, your father is not obliged to provide for you, and therefore he is not obliged to pay Zakat al-Fitr on your behalf; rather, you should pay it for yourself.