If you are driving down to San Diego on a Friday after work, and you can get someone to drop you off at LGB on Friday morning, you may be able to get a one-way rental on a reasonable weekend rate. As an example, for pickup on Friday 19 December 2014 at 9:00 AM at LGB, and return by Saturday 20 December at 9:00 AM at SAN, Avis is under $30 using AWD 108392 (Costco) with the Pay Now option.
With a rental car, you won't be limited to the Amtrak schedule, and you could drive down in the early morning hours before your flight and avoid the overnight in San Diego. If you do drive down in the late night or early morning hours, be sure to check CalTrans for scheduled road construction at
http://www.dot.ca.gov/hq/roadinfo/plannedwork.htm and plan accordingly.
The return part is harder to find a reasonable one-way rental from LAX to LGB (or your neighborhood location) since it sounds like you are coming back on a weekday.