The business center doesn't open until like 6:30 or 7 or something.
Most resorts have those phone/web things. You can't print, but you can "pretend" to print, get your seat assignment (the important thing), then print a "duplicate" pass at the airport.
That was what we did and it worked great. We had a party of six, which was difficult to seat together, so getting up early for seat assignments was important.