I am afraid that I am not going to be of much help here. Most of my research has been for merchant ships in the Pacific Theater. I have very little info on John Banvard. She was at Anzio as part of Operation SHINGLE, stayed in the area until February 1 when she had completed unloading. On January 26 she was victim of a near miss by a glider bomb, and the crew abandoned ship. As far as I can tell, any troops she carried had already been disembarked by that time. She suffered little damage and the crew was returned to the ship the next day.
It wasn't clear from your post if you knew your father was on the Banvard at Anzio, or if you assumed that since he was on her in November going to Algiers. It was not at all uncommon for army troops to be transported on different ships if they spent any time at an intermediate port. I just don't have more info on Banvard's movement during this period.
Sorry I can't be of much help here.