Find Pandas column largest/smallest values where dates don't overlap

Question

I have a DataFrame like:

df = pd.DataFrame(index = [0,1,2,3,4,5])
df['XYZ'] = [2, 8, 6, 5, 9, 10]
df['Date2'] = ["2005-01-06", "2005-01-07", "2005-01-08", "1994-06-08", "1999-06-15", "2005-01-09"]
df['Date1'] = ["2005-01-02", "2005-01-03", "2005-01-04", "1994-06-04", "1999-06-12", "2005-01-05"]
df['Date1'] = pd.to_datetime(df['Date1'])
df['Date2'] = pd.to_datetime(df['Date2'])

I need to follow the 2 largest values of XYZ with dates that do not overlap. The expected output would be:

XYZ   Date1       Date2
10    2005-01-05  2005-01-09
9     1999-06-12  1999-06-15
5     1994-06-04  1994-06-08

I tried to sort by "XYZ":

df.sort_values(by="XYZ", ascending=False, inplace=True)

And then compare dates:

df['overlap'] = (df['Date1] <= df['Date2'].shift()) & (df['Date2'] >= df['Date1'].shift())

And then drop any True values in df['overlap'] and take the nlargest() values, however that results in cases that do overlap.

Any help would be much appreciated.