Interesting discovery:

Last night - I had the error exactly as above. I tried to make a new booking, and it showed precisely one seat available (Seat map and booking capacity both).

Today - I tried to check in again just to see, and it told me "As there are no seats available on this flight, you may proceed with your original seat selection". I was able to continue with the check in, except no boarding pass printing permitted.

So it seems to me this is a really stupid big wherein TK wants to allow you to change your seats, but if the number of empty seats is fewer than the number in your party, it thinks you won't be able to change enough seats, so it says no dice. But if the number of empty seats is 0, then no seat changes are possible, so you can go ahead and check in and the step gets skipped.