I figured easiest would be getting the Amtrak from LA Union Station to San Diego, but have discovered all trains on March 31 are carry on only, no checked luggage (we have 3 suitcases in addition to all our carry on bags)
That just means "no porters", you'll have to DIY-muscle your bags onto the coach yourselves.
Amtrak doesn't care about baggage (or weight for science reasons*). Plenty of room.
The real winner here is the Tijuana Trolley, which goes directly from the San Diego Amtrak (Santa Fe station) to the border crossing at Tijuana. One seat ride, $2.50 fare, huge asterisk. That is just regular old suburban public transit, obviously no porters. And your party will take a ridiculously outsize amount of space compared to actual commuters, but that happens a lot on that trolley. Just don't do it during the outbound commute (4-7 pm).
Such an elegant solution to that transportation link. San Diego really outdid themselves. Amtrak is actually fairly hard to get to from LAX, but if you can find a more direct way to get to San Diego Amtrak ("Santa Fe station"), feel free to do it.
The huge asterisk: The Trolley uses a "proof of payment" system in which you must obtain some sort of ticket or e-ticket before you board. This is a limited-time typically 2-hour "pass" which entitles you to be on the system. Note that some tickets are sold "not activated" so you can pay now and activate later; these must be activated - don't forget!
Honestly, the app may be the path of least resistance, as otherwise they'll sell you a permanent physical transit card that only works in San Diego. The physical card doesn't require you to set up an account, you can do it "anonymously". However, each person needs their own card or app - one person can hold the cards, but there must be a separate card or app for each person. There is no way to put 2 activated fares on one card or app.
Fare inspectors will randomly check trains and give $300 fines for fare evasion to honest newcomers looking for someone to pay. I'm not kidding. That's real. It's a Federal program subsidized by Ford and Toyota to make sure no new riders ever take public transit, OK I'm kidding about that. But really, it does seem like that.
Wow, this just turned into a warning against the Tijuana Trolley.
* Trains don't have induced drag thanks to Mr. Timken, so weight does not add any significant fuel cost. (actually it takes more fuel to haul an empty coal train than a full one, since the coal acts as a fairing to keep the empty hoppers from scooping air).