I am flying from LAX to TPE on Thursday, March 8. I and my travel companion are currently in row 58 H/K, one of the best two-some seats according to seatguru.com. I checked in online, and noticed that 2/3 of the seats are taken, and there are several rows with all three seats available (meaning it doesn't appear that the flight is sold out when looking at the seat map). I would prefer to have an open middle seat, but I would risk having somebody take that middle seat later (if it is a full flight). I then started booking the same flight on the SQ website, and the flight is displayed as not available. Does this mean that this flight is sold out? I thought that everybody, with the few exceptions, receive automatic seat assignments by SQ at the 48 hour check-in window.

QUESTIONS:
1. Is the seat map showing 1/3 of the seats unassigned or the fact that I couldn't book that flight anymore a better indication on whether the flight is full? Based on what I described above, does it look like the flight is sold out?

2. Does it look like I'll have a good chance of scoring an empty middle seat if I change to a three-some row?

Thanks!