Your TA is incorrect about the stopovers:
F. TRAVEL MAY ORIGINATE AT ANY POINT FOR WHICH FARES ARE PUBLISHED AND MUST TERMINATE AT THE SAME POINT OR AN INTERMEDIATE POINT IN THE COUNTRY OF ORIGIN.
--- A MAXIMUM OF ONE STOPOVER IN COUNTRY OF ORIGIN. --- A MAXIMUM OF TWO FREE STOPOVERS PER REGION - SWP/ ASIA/NORTH AMERICA/SOUTH AMERICA. ---
--- WHERE A PASSENGER DISEMBARKS AT ONE POINT AND RE-EMBARKS AT A SUBSEQUENT POINT ENROUTE THE POINTS COUNT AS A SINGLE STOPOVER. ---
You do not have to return to the port of origin and it should not count as a stopover if you do not as there is no "RE-EMBARK"-ation in that case.
However, there is another impediment. Your LAS-LAX surface segment is included in the
total Distance and puts it over the 26000 miles.