Can you help recommend an insulation upgrade for my 150-year-old home?

I agree with your concern that moisture sometimes gets in through board-and-batten siding under conditions of driving rain. Fiberglass insulation batts within your wall cavities would only encourage rot should this happen, while fitting rigid foam boards within wall framing is difficult and impractical. That leaves spray-on foam, and I think it’s a good choice in your case. I first saw large amounts of this material in action on a commercial building project in the late 1980s. Polyurethane foam is rigid enough to cling firmly to its surroundings, yet not so tough that it can’t move a little here and there. Based on this and similar experiences, I don’t think you need to worry about spray-on foam causing cracks in your siding. You can try some experiments with hand-held spray cans of the foam as it’s sold to fill cracks in various home-related situations, just to be sure. But application of this foam in your case only makes sense if you’ll be removing the interior plaster or wall board, revealing an open wall frame cavity inside. With all this in mind, I think spray foam can do a great job for you. Besides its impressive insulation value, polyurethane foam seals out drafts completely while being impervious to water. The only drawback is cost, which is high. Shop around for quotes from at least three application companies.