I don't know.

On most trains I've been on, on board bikes can go on a hook in the baggage car (some also have them in the cars but I've done those less). So my guess is the 2" is related to the dimension of the hook and if you have a tire large enough it doesn't fit on the hook then there will be an issue. If it is 2.25" and fits fine on the hook.... less sure there.

Checked baggage also goes in the baggage car. Amtrak sells bike boxes that are *big* compared to most all airline boxes. I'm 6' 4" and my bike fits easily in an Amtrak box with both wheels on and pedals removed and handlebars taken off.

In slightly smaller airline boxes, I also remove the front wheel and sometimes turn my stem so it points be backwards. In the smallest airline boxes, both wheels come off.

My suggestion would be to go down to the San Diego station and see if they will sell you a box in advance of your trip. If so, see if you can break down the bike enough to fit in the box. If so, travel with Amtrak using one of their boxes. Note however that not every station is a baggage station where they open the baggage car (one way you can sort of tell is to make a trial booking and add the $20 for a bike... If it tells you no bike spots are available when a longer trip to a major station would let you add a bike .... then most likely one of the stops isn't a baggage stop).

Also note that there can be differences between individual trains and the general guidelines are a good starting point but exactly where the bike is placed and individual conductor behavior will differ between trains. In the last few years, I've taken long haul trains mostly in western US and gradually the bike hook in baggage car method has been added to those trains.