certainly DB is a better experience than any USA train, no argument
i did travel friday afternoon, and was only able to get a table seat
being over six foot, i found it super tight- like the LIRR
and since every sq.cm. was filled with passengers or luggage it was brutally claustrophobic- and hot and steamy
the snack cart could not make it through the cars due to the crowds
but yes, sunday mornings should be lightly traveled
did you look for another airport to fly into in europe other than FRA with a better bari connection?
there are morning flites from BRU, FCU, MUC, MXP, any of which will be less of a hassle than going to CGN