Hi John - I love the sound of your adventure, to ride the train across the country and then bike back. Good for you.
AMTRAK trains run up and down California, Oregon, and Washington. However, with only a few exceptions, the train stops are far from the ocean, usually with at least one mountain range, and sometimes a hundred miles of biking on chancy roads to get to the coast. You are well advised to be aware of which stops have baggage service, and which do not.
There is also AMTRAK bus service, which looks like it runs up and down US-101 in California, but I do not have first hand knowledge of it.
If you do decide to take the train to the San Francisco Bay area, be aware that the AMTRAK trains actually stop in Emeryville, Oakland and San Jose, but not San Francisco. It should be possible to get off AMTRAK in Oakland and catch a BART train under the bay to San Francisco. From there, a rider would be only a few urban miles from the PCH route (Map 3). But, you would need to carefully plan how to manage and protect your bike and baggage on the train. I think there may also be ferries.
Further north, Portland and the stops up to Seattle are also options, as long as baggage service is supported. From both Portland and Seattle, there are well beaten paths to the Pacific Coast Route. Seattle is only a ferry ride away from Bremerton. Portland is a hard days' ride (for us) to either Sea Side or Astoria.
If I do the Pacific Coast again, I will certainly revisit the Oregon Coast. It is spectacular, the towns are spaced at bikeable distances from each other, and the shoulders are usually ample and safer (although there are always exceptions). The most famous stretch of the California coast is from Santa Cruz to San Luis Obispo. So detraining in the San Francisco Bay Area would make it easy to get to Santa Cruz in a day or two by bike.
I do not know that would fit with your plan to hook up with the Southern Tier to get home. Something to consider, in southern California, is that AMTRAK does have stations in San Luis Obispo, Los Angeles, and San Diego.