First-time Amtrak rider here and I'm looking into booking a 2-zone RT award EUG-CHI and trying to get the most mileage/scenery for the buck. Going to CHI I see a CS option down to LA and then the Texas Eagle up to CHI. But I see that there is only a 1 hour connection time in LA. From reading all these threads I get the distinct feeling Amtrak isn't always on time

. So I'm wondering if anyone wants to give me odds on successively making it on time to catch the TE. If my odds aren't good, just wondering what the Amtrak protocol is for such missed connections: Do they put me on the next available TE? Or do they not care which particular route I was originally booked on and only care about my final destination and would just put me on a Southwest Chief (for example) if that's available sooner? Or am I offered a choice of available options? So many questions. I wouldn't be too worried if I didn't have hotel and plans for a particular day's arrival, but I will have, and it appears to me that if I miss that TE connection, that will mean an overnight in LA. Not optimum.
So any help/advice from the Amtrak experts out there would be much appreciated.