I am too very interested in playing the music on period instruments. Have no tips regarding adresses in the San Francisco Bay area, however.
But there is a revival of custom built instruments in historic manner. Since some instruments like the clavichord (the most beloved keyboard instrument from Bach, and also Haynd, Mozart, even Brahms liked to play on a clavichord) are surprisingly easy to build, so there are kits available to build an own. If I anytime buy a kit for an own built clavichord I for sure will present it here along with some Bach WTC items recorded on it.
Here is a link for such kits:
But instead building an own it is also possible to try out such an instrument in a regional association. So it should be possible to play on new built fortepianos or harpsichords or clavichords.
For instance in Los Angeles, they do have an original 1841 Broadwood piano e.g. to play on, and chances are good that there are older instruments as well: