Punta Arenas to Puerto Natales at midnight?

We arrive at Punta Arenas at 11:59 pm on the 13th and plan to go to Puerto Natales as soon as we can to catch the 7:30am bus to El Calafate. It appears we will miss the last bus from PA to PN and will have to wait 7 hrs (until 7am) to get the next bus out. Are there any taxi or mini bus options that leave PA to PN earlier to get us there before 7:30am? If not, is there a hotel in PA you recommend where we can check in around midnight if we decide not to wait 7 hours?

Second question: I tried to buy bus tickets online but was unsuccessful. What is the most efficient way to get tickets in PA after our flight arrives at midnight?

Thanks in advance!

Thanks

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