I'd have to recommend giving the SWC some consideration for the eastbound trip. While the scenery is not a consistently spectacular as the CZ, it is better overall than the EB IMHO (yes, Glacier is beautiful but you are out of there around 10am and the rest of the day is spent in eastern Montana, which can be considered West Dakota for scenic interest). SWC has red rock country around Gallup, Glorietta and Raton passes.
SWC is also likely to be rerouted in the fairly near future because BNSF no longer uses Raton Pass and won't maintain it after the current contract is up. So if you have any interest in that route, ride it now, it may not be around much longer. The potential new route, the Transcon via Amarillo, is not as scenic.
There is a lot to do in LA, even just on public transit. Right by the station you have Olvera St, you have Phillipe's to have breakfast or lunch at. You can take the Red Line to Hollywood and Highland if that interests you. If you have a hankering for an In 'N Out burger, there's one near Sunset and Highland you can walk to from Hollywood and Highland. You can go to Long Beach on the Blue Line, or you can just take a busman's holiday and ride some of the various Metrolink lines.
LAUS's baggage room will hold bags for $4(?) bag.
Not sure how you may be planning to get to LA from the Bay Area off the CZ. You have to overnight somewhere to get to LA. You can come down from the Bay Area via the San Joaquin/bus connection in the morning and make the SWC connection that evening.