The general rule of thumb is that older bikes with 'traditional' geometry are easier to make work in larger sizes than a modern frame, so Spagetti Legs' suggestion that you could probably handle a 57 cm frame, even though your fitter suggested 52-54, may well be right. I suspect your Dad's frame is a lot bigger than that, though. Definitely do some seat tube and top tube measurements.

If you can afford it, I'd do a combo of what the others have suggested: hang your father's frame as a piece of art, find a matching frame in your size, put your Dad's old components on it, and enjoy having your cake and eating it too.