For now I added a bunch of labels with empty strings to fill the whole thing up. I add a panel to the contentPane, in which I add a panel for the labels, and one for the textfields. Here's my code:
You may need another layout. You could try GridBag, with insets round the JTextFields, or Google for MigLayout.
You may be able to set sizes on the JTextFields; they probably have several methods like setXXXSize.
I adjusted and compiled the code you posted, and it works. Is it because you left the default layout for JPanel instead of giving it a GridLayout? Maybe I have to fiddle some more with that and see what works and what not...