Does this trip count for the commercial 300NM cross country requirement?
Yes.  It counts.  One leg needs to be at least 250NM and you have a 280NM leg.

§61.129   Aeronautical experience.
(4) Ten hours of solo flight time in a single engine airplane

(i) One cross-country flight of not less than 300 nautical miles total distance, with landings at a minimum of three points, one of which is a straight-line distance of at least 250 nautical miles from the original departure point. However, if this requirement is being met in Hawaii, the longest segment need only have a straight-line distance of at least 150 nautical miles;