Hi Dennis, welcome to the forum.
I suspect there are too many unknowns when working with wood. The spacing between annual-rings can be so different as could the soft-spots and hard spots within the single piece of wood, that frequencies could range from nothing to a zillion, well almost. Feed rates would also have to come into it when considering vibration and the control thereof.
I would suggest working from the back forwards with trial and error. What's the largest diameter or area of cross-section of the bar that you can accommodate? I would then use that size as the max size for the boring-bar.
From there you could advance up the stiffness scale of various metals. That scale is usually pretty proportional with cost. The more rigid the material, the higher the cost.
Solid Silicon Carbide boring bars are commonly used in metalworking, but depending on diameter (or cross-sectional area) it can get expensive fast.
If you are boring to differing depths from one project to the next, you could mount the bar in a holder that will allow more or less overhang/cantilever. Just sufficient sticking out to reach the desired depth.