Long story short:
Schedule change on an existing ticket, booked in First Class (Z fare, Reserve Companion Cert).
Since I don't have any other certs, I cannot use delta.com to find alternatives. The "change flight" on DL website shows nothing available.

I found this post and tried using ITA Matrix to find alternatives:
https://www.reddit.com/r/delta/comme...flights_using/

However, ITA is returning flights that neither .com NOR the Silver Medallion Agents can find/see, so possibly I'm doing something wrong.
For example:
Both dl.com (if I do the "change flight") and rep said no other options for 4/25/26 LGA-EYW (other than the now changed to EJ170 direct flight).
However, ITA shows there's several flights such as the 6:00 am to ATL to EYW at 1:44 pm

Same goes for different airports (yes, I know there would be a fare difference):
JFK - EYW, matrix shows like 6 non-overnight flights, but rep says there's only one and it gets in at 10:27 pm

Am I reading the results wrong, or not doing something properly with Matrix? Or do I need to HUCA and get a different agent?