There is a very simple way: just create a new dataframe based on the original, with the correct order of multiindex columns:
multi_tuples = [('IWWGCW',24), ('IWWGCW',48), ('IWWGDW',24), ('IWWGDW',48)
, ('BASE',24), ('BASE',48)]
multi_cols = pd.MultiIndex.from_tuples(multi_tuples, names=['Experiment', 'Lead Time'])
df_ordered_multi_cols = pd.DataFrame(df_ori, columns=multi_cols)