It closes at 7 every night till the 6th .. then the 6pm closing starts for a week or so till the 5pm time starts.
Anyway.. you'll have plenty of time between park closing and your ADRs. AKL has a bus exclusive to them... it's only about 15 minutes from boarding till the resort.. if that much.
Not sure if you know it but MMHs for AK is the next morning (the 2nd). That was pretty crowded when we went. We got FPs for Everest because it didn't open for about 2 hours! Technical problems. We got our FPs about 8:15 or 20.. and they were for 2:05 !!..lol.
Night magic hours is awesome there! All the animals seemed to be out.. and the wait for Everest was only 15-20 minutes during the last 1.5 hours! Don't know if that's usual, but it was like that the night we were there. They have EMHs on the 7th. Take the Maharaja Jungle Trek while you wait (it's right before the Siamang apes structure).. the 'ruins' and murals are really nice. They have tigers and .. UGH.. HUGE fruit bats! lol.. my dd loved it! There was also an aviary.. they give you a chart of the birds you will see.. and you do see them! They're everywhere!
Oh.. try the pina colava at Victoria Falls while you wait for your ADRs for Boma... yummy!
Sigh.. I love AK... and AKL