Problem is in "split 2" atribute. By passing that attribute you are splitting cells where JLabels are. So one JLabel and one JTextField fits in one cell. Since JLabels have different sizes (during different length of text) you have that effect of nonequal space.
This should solve problem:
contentPane.setLayout(new MigLayout("center"));
contentPane.add(lbl1, "alignx trailing");
contentPane.add(txt1, " wrap");
contentPane.add(lbl2, "alignx trailing");
contentPane.add(txt2, "wrap");
contentPane.add(lbl3, "alignx trailing");
contentPane.add(txt3, " wrap");
contentPane.add(lbl4, "alignx trailing");
contentPane.add(txt4, " wrap");
contentPane.add(btn5, "skip, split2, growx");
contentPane.add(btn6,"growx");