That’s a great woodworking question. There’s no need to increase thickness on larger parts, but there are two things you should consider for other areas. First, and most importantly, don’t allow knots to be present in any of the thin slats that are characteristic of this style. You may need to use a higher grade of pine for these parts. Also, as you build, cut test samples of the smaller parts, and flex them by hand. Use your judgment to determine if they’re too flimsy, and to decide how best to beef them up (either by increasing thickness or width). The challenge will be arriving at a strong design, while at the same time not throwing the traditional Mission proportions out of whack. Given the price of oak, I think this exercise is worthwhile.