Slightly different circumstance, and specific, but I have twice changed flights between SFO and LAX online on the day of flight (e.g., two hours before the one I was changing to) and still got the $39 "Internet Only" fare. Thank you Southwest for engaging Virgin.
In the first instance, I was also glad to learn that one can change a flight after OLCI the day before. Hoo boy!

!
(And with the light loads between this pair, still get good seats.)