LAX GAs have generally been good about the boarding process. Yesterday as a GLARING exception. Flight 144 was running a bit late due to a 30-minute late arrival of the inbound. The departure board remained posted at the original departure time. I was #1 on the upgrade list, with EF going from F0 to F1/A1 90 minutes before flight time (checked again in gate area). Normally, if they're going to upgrade folks, they do it within 20 minutes of scheduled departure time. Instead of following the current "First class and EXP" process, the GA boarded F first and enforced non-boarding of EXPs. Then they called PLT and EXP. Since it was a FULL flight, and the usual "first class is full" announcement was made, I went ahead and boarded to my exit-aisle seat. Better to snag the bin space than gate-check a bag. Good choice - this was a 737 with the Sky interior (and the new bins). Folks couldn't figure out how to put bags in. It took 45+ minutes to board the plane. I call it "excruciating". After *everyone* was on board, including the full Y cabin, they came on board, called me to the front, and gave me the empty seat in F. Of course, the F bins were haphazardly full, and it took a couple of extra minutes to rearrange them. Too late to get a pre-departure drink. Oh well. Clearing me late also meant that someone who might have wanted an exit row in back didn't get to sit there. Flight was otherwise good, except we ended up being an hour late in arrival, even though the inbound was only 30 minutes. Cabin crew was DC based, and had a couple of folks that recently came down from Boston.