Don't worry about the timeliness of the Lake Shore. As I mentioned in another thread, while it's possible that it will be so late as to miss connections, it is rare that it will happen. It usually takes something major like a freight train derailment to make the train that late. Again, no guarantees, but don't worry about it right now. Also, I'll note that if you are on the Lake Shore and you do happen to be very late, the staff in Chicago will take care of you. Some have tried calling reservations while still on the (late) train and changed their trip around, which pretty much invalidates any reaccommodation that the CHI staff could do for you. Of course, there aren't any guarantees that you'll get a sleeper, unfortunately (as you have seen, they do sell out and are a hot commodity), but you will get to your destination.
The Texas Eagle sleeper overnights in San Antonio before continuing on to Los Angeles as part of the Sunset Limited. Again, it would take some major disaster to miss that connection, and what usually happens in that case (major disaster) is that they'll put passengers on a bus to catch up. Not fun, but again, the priority is on getting you to your destination. Again, that case is very rare.
The Sunset Limited has pretty good on-time performance (it used to be the worst in the system, but thanks to some better dispatcher handling, lower traffic, oh, and a ton more schedule padding, it now ranks near the top of the LD trains).
Your LA-San Diego ticket is valid on any train between those two cities, so if you miss the train you wanted to catch, just hop on the next one. The only exception to that is if you reserved business class, then technically it's only good on the specific train you reserved. However, in reality, you can still use the same ticket on any other trip, and odds are pretty good (though no guarantees) that as long as there's room in business class on the train you take, they'll let you ride in that car anyway. If you haven't reserved business class, then don't worry about it (it's not really worth all that much other than to be in an "exclusive" car with 80 other people and get a free drink and snack box).